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1.	Ekström, Erik, 1989- (författare) Growth and thermoelectric properties of CaMnO3-based thin films 2018 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract The field of them1oelectrics started in early 19th century. Since the discovery of the Seebeck effect and the Peltier effect, thermoelectric modules have found their way into, mostly, niche applications such as radioisotope thermoelectric generators on space missions. Thermoelectric modules can also be used for cooling, utilizing the Peltier effect.Thermoelectrics are promising materials due to the operation nature of the modules. That is, they have no moving parts, no exhaust, long lifetime without maintenance, features that make them attractive for many applications. Despite these promising properties, thermoelectric modules are mostly used in niche applications. The main reason for this is conventional modules with the highest efficiency are commonly made of expensive and/or rare elements which prevents mass production.To tackle this problem, new materials are investigated to find a module that can be made widely available. Oxides are one possibility, where an added benefit is that they are chemically stable even at elevated temperature. The perovskite CaMnO3 is one of the more promising oxides, with elements that are abundant on earth and cheap. The material does suffer from low electrical conductivity which results in a low electrical conductivity and efficiency. A substantial effort has been put in to increase the efficiency of CaMnO3, hut it still needs improvement.In my thesis, I have investigated the CaMnO3 system. CaMnO3 was synthesized using co-reactive RF-magnetron sputtering and post annealing. The synthesis method is already known hut has not been used for deposition of perovskites. I have also demonstrated that this synthesis method can be used to dope CaMnO3 with niobium at appropriate levels for enhancing the efficiency.
2.	Bayraktar, Erhan, et al. (författare) Disorder detection with costly observations 2022 Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:2, s. 338-349 Tidskriftsartikel (refereegranskat)abstract We study the Wiener disorder detection problem where each observation is associated with a positive cost. In this setting, a strategy is a pair consisting of a sequence of observation times and a stopping time corresponding to the declaration of disorder. We characterize the minimal cost of the disorder problem with costly observations as the unique fixed point of a certain jump operator, and we determine the optimal strategy.
3.	Bogoya, Manuel, et al. (författare) Matrix-less methods for the spectral approximation of large non-Hermitian Toeplitz matrices : A concise theoretical analysis and a numerical study 2024 Ingår i: Numerical Linear Algebra with Applications. - : Wiley. - 1070-5325 .- 1099-1506. Tidskriftsartikel (refereegranskat)abstract It is known that the generating function of a sequence of Toeplitz matrices may not describe the asymptotic distribution of the eigenvalues of the considered matrix sequence in the non-Hermitian setting. In a recent work, under the assumption that the eigenvalues are real, admitting an asymptotic expansion whose first term is the distribution function, fast algorithms computing all the spectra were proposed in different settings. In the current work, we extend this idea to non-Hermitian Toeplitz matrices with complex eigenvalues, in the case where the range of the generating function does not disconnect the complex field or the limiting set of the spectra, as the matrix-size tends to infinity, has one nonclosed analytic arc. For a generating function having a power singularity, we prove the existence of an asymptotic expansion, that can be used as a theoretical base for the respective numerical algorithm. Different generating functions are explored, highlighting different numerical and theoretical aspects; for example, non-Hermitian and complex symmetric matrix sequences, the reconstruction of the generating function, a consistent eigenvalue ordering, the requirements of high-precision data types. Several numerical experiments are reported and critically discussed, and avenues of possible future research are presented.
4.	Bolten, Matthias, et al. (författare) A note on the spectral analysis of matrix sequences via GLT momentary symbols : from all-at-once solution of parabolic problems to distributed fractional order matrices 2023 Ingår i: Electronic Transactions on Numerical Analysis. - : Osterreichische Akademie der Wissenschaften, Verlag. - 1068-9613. ; 58, s. 136-163 Tidskriftsartikel (refereegranskat)abstract The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization of a parabolic diffusion problem using a space-time grid and secondly from the approximation of distributed-order fractional equations. For this purpose we use the classical GLT theory and the new concept of GLT momentary symbols. The first permits us to describe the singular value or eigenvalue asymptotic distribution of the sequence of the coefficient matrices. The latter permits us to derive a function that describes the singular value or eigenvalue distribution of the matrix of the sequence, even for small matrix sizes, but under given assumptions. The paper is concluded with a list of open problems, including the use of our machinery in the study of iteration matrices, especially those concerning multigrid-type techniques.
5.	Bolten, Matthias, et al. (författare) Toeplitz momentary symbols : definition, results, and limitations in the spectral analysis of structured matrices 2022 Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 651, s. 51-82 Tidskriftsartikel (refereegranskat)abstract A powerful tool for analyzing and approximating the singular values and eigenvalues of structured matrices is the theory of Generalized Locally Toeplitz (GLT) sequences. By the GLT theory one can derive a function, called the symbol, which describes the singular value or the eigenvalue distribution of the sequence, the latter under precise assumptions. However, for small values of the matrix-size of the considered sequence, the approximations may not be as good as it is desirable, since in the construction of the GLT symbol one disregards small norm and low-rank perturbations. On the other hand, Local Fourier Analysis (LFA) can be used to construct polynomial symbols in a similar manner for discretizations, where the geometric information is present, but the small norm perturbations are retained. The main focus of this paper is the introduction of the concept of sequence of "Toeplitz momentary symbols", associated with a given sequence of truncated Toeplitz-like matrices. We construct the symbol in the same way as in the GLT theory, but we keep the information of the small norm contributions. The low-rank contributions are still disregarded, and we give an idea on the reason why this is negligible in certain cases and why it is not in other cases, being aware that in presence of high nonnormality the same low-rank perturbation can produce a dramatic change in the eigenvalue distribution. Moreover, a difference with respect to the LFA symbols is that GLT symbols and Toeplitz momentary symbols are more general -just Lebesgue measurable -and are applicable to a larger class of matrices, while in the LFA setting only trigonometric polynomials are considered and more specifically those related to the approximation stencils. We show the applicability of the approach which leads to higher accuracy in some cases, when approximating the singular values and eigenvalues of Toeplitz-like matrices using Toeplitz momentary symbols, compared with the GLT symbol. Finally, since for many applications and their analysis it is often necessary to consider non-square Toeplitz matrices, we formalize and provide some useful definitions, applicable for non-square Toeplitz momentary symbols.
6.	Coco, Armando, et al. (författare) Spectral and norm estimates for matrix-sequences arising from a finite difference approximation of elliptic operators 2023 Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 667, s. 10-43 Tidskriftsartikel (refereegranskat)abstract When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for matrix-sequences arising from the approximation of the Laplacian via ad hoc finite differences. The analysis involves several tools from matrix theory and in particular from the setting of Toeplitz operators and Generalized Locally Toeplitz matrix-sequences. Several numerical experiments are conducted, which confirm the correctness of the theoretical findings.
7.	Dareiotis, Konstantinos, et al. (författare) Density symmetries for a class of 2-D diffusions with applications to finance 2019 Ingår i: Stochastic Processes and their Applications. - : ELSEVIER SCIENCE BV. - 0304-4149 .- 1879-209X. ; 129:2, s. 452-472 Tidskriftsartikel (refereegranskat)abstract We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding forward Kolmogorov equation problematic. We overcome this by extending a classical symmetry result for densities of one-dimensional diffusions to our case, thereby reducing the study of forward equations with exploding boundary data to the study of a related backward equation with non-exploding boundary data. We also discuss applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models. (C) 2018 Elsevier B.V. All rights reserved.
8.	De Angelis, Tiziano, et al. (författare) Dynkin Games with Incomplete and Asymmetric Information 2022 Ingår i: Mathematics of Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0364-765X .- 1526-5471. ; 47:1, s. 560-586 Tidskriftsartikel (refereegranskat)abstract We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian setup, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result that allows us to find the value of the game and players' optimal strategies by solving suitable quasi-variational inequalities with some nonstandard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasi-variational inequalities can be obtained.
9.	De Angelis, Tiziano, et al. (författare) Playing with ghosts in a Dynkin game 2020 Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149 .- 1879-209X. ; 130:10, s. 6133-6156 Tidskriftsartikel (refereegranskat)abstract We study a class of two-player optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that if the underlying process is a R-d-valued, continuous, strong Markov process, and the stopping payoff is a continuous function (with mild integrability properties) there exists a Nash equilibrium in randomised stopping times for the game. Moreover, the equilibrium strategies and the expected payoffs of the two players are computed explicitly in terms of the corresponding one-player game. To the best of our knowledge this is the first paper to address this version of Dynkin games.
10.	De Angelis, Tiziano, et al. (författare) The dividend problem with a finite horizon 2017 Ingår i: The Annals of Applied Probability. - : INST MATHEMATICAL STATISTICS. - 1050-5164 .- 2168-8737. ; 27:6, s. 3525-3546 Tidskriftsartikel (refereegranskat)abstract We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at 0 and created at a rate proportional to its local time.
11.	De Angelis, Tiziano, et al. (författare) The maximality principle in singular control with absorption and its applications to the dividend problem 2024 Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 62:1, s. 91-117 Tidskriftsartikel (refereegranskat)abstract Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with twodimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm's (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
12.	Dyrssen, Hannah, et al. (författare) Sequential testing of a Wiener process with costly observations 2018 Ingår i: Sequential Analysis. - : TAYLOR & FRANCIS INC. - 0747-4946 .- 1532-4176. ; 37:1, s. 47-58 Tidskriftsartikel (refereegranskat)abstract We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time but also, if continuing, how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.
13.	Ekström, Erik, 1977-, et al. (författare) A detection problem with a monotone observation rate 2024 Ingår i: Stochastic Processes and their Applications. - : Elsevier. - 0304-4149 .- 1879-209X. ; 172 Tidskriftsartikel (refereegranskat)abstract We study a quickest detection problem where the observation rate of the underlying process can be increased at any time for higher precision, but at an observation cost that grows linearly in the observation rate. This leads to a problem of combined control-and-stopping with incomplete information, with a two-dimensional sufficient statistic comprised of the current observation rate together with the conditional probability that disorder has already happened. The problem is shown to have a semi-explicit solution, where for some parameter values it is too costly to exert control at all, whereas for other parameter values the optimal strategy is to increase the observation rate in such a way that the sufficient statistic reflects at a certain boundary until the optimal stopping time. In both cases we fully characterise the optimal strategy with the help of appropriate smooth fit conditions.
14.	Ekström, Erik, 1977-, et al. (författare) A renewal theory approach to two-state switching problems with infinite values 2020 Ingår i: Journal of Applied Probability. - : CAMBRIDGE UNIV PRESS. - 0021-9002 .- 1475-6072. ; 57:1, s. 1-18 Tidskriftsartikel (refereegranskat)abstract We study a renewal theory approach to perpetual two-state switching problems with infinite value functions. Since the corresponding value functions are infinite, the problems fall outside the standard class of problems which can be analyzed using dynamic programming. Instead, we propose an alternative formulation of optimal switching theory in which optimality of a strategy is defined in terms of its long-term mean return, which can be determined using renewal theory. The approach is illustrated by examples in connection with trend-following strategies in finance.
15.	Ekström, Erik, 1977-, et al. (författare) A sequential estimation problem with control and discretionary stopping 2022 Ingår i: PROBABILITY UNCERTAINTY AND QUANTITATIVE RISK. - : American Institute of Mathematical Sciences. - 2095-9672 .- 2367-0126. ; 7:3, s. 151-168 Tidskriftsartikel (refereegranskat)abstract We show that " full-bang " control is optimal in a problem which combines features of (i) sequential least-squares estimation with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded control of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) " fast " discretionary stopping. We develop also the optimal filtering and stopping rules in this context.
16.	Ekström, Erik, 1977- (författare) American Options And Incomplete Information 2019 Ingår i: International Journal of Theoretical and Applied Finance. - 0219-0249. ; 22:6 Tidskriftsartikel (refereegranskat)abstract We study the optimal exercise of American options under incomplete information about the drift of the underlying process, and we show that quite unexpected phenomena may occur. In fact, certain parameter values give rise to stopping regions very different from the standard case of complete information. For example, we show that for the American put (call) option it is sometimes optimal to exercise the option when the underlying process reaches an upper (lower) boundary.
17.	Ekström, Erik, 1977-, et al. (författare) Auctions with an Invitation Cost 2021 Ingår i: International Game Theory Review. - : World Scientific. - 0219-1989. ; 23:1 Tidskriftsartikel (refereegranskat)abstract We consider an auction in which a seller invites potential buyers to a sealed-bid first-price auction, without disclosing to the buyers the number of extended invitations. In the presence of a fixed invitation cost for each invited bidder, the whole auction can be described as a game, where the set of players consists of all bidders together with the seller. In a setting with fully observable common values we show the existence of a Nash equilibrium in mixed strategies. In this equilibrium, the seller should invite precisely one or two potential buyers with certain probabilities, and each invited buyer should place a randomized bid according to a certain distribution.
18.	Ekström, Erik, 1977-, et al. (författare) Bayesian sequential least-squares estimation for the drift of a Wiener process 2022 Ingår i: Stochastic Processes and their Applications. - : Elsevier. - 0304-4149 .- 1879-209X. ; 145, s. 335-352 Tidskriftsartikel (refereegranskat)abstract Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known "prior " distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, we provide conditions on the prior distribution that guarantee a one-sided stopping region. Lastly, some concrete prior distributions are studied to illustrate the theoretical results.
19.	Ekström, Erik, 1977-, et al. (författare) Boundary conditions for the single-factor term structure equation 2011 Ingår i: The Annals of Applied Probability. - 1050-5164 .- 2168-8737. ; 21:1, s. 332-350 Tidskriftsartikel (refereegranskat)abstract We study the term structure equation for single-factor models that predict nonnegative short rates. In particular, we show that the price of a bond or a bond option is the unique classical solution to a parabolic differential equation with a certain boundary behavior for vanishing values of the short rate. If the boundary is attainable then this boundary behavior serves as a boundary condition and guarantees uniqueness of solutions. On the other hand, if the boundary is nonattainable then the boundary behavior is not needed to guarantee uniqueness but it is nevertheless very useful, for instance, from a numerical perspective.
20.	Ekström, Erik, 1977- (författare) Bounds for perpetual American option prices in a jump-diffusion model 2006 Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 43:3, s. 867-873 Tidskriftsartikel (refereegranskat)abstract We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.
21.	Ekström, Erik, 1977-, et al. (författare) Bubbles, convexity and the Black-Scholes equation 2009 Ingår i: The Annals of Applied Probability. - 1050-5164 .- 2168-8737. ; 19:4, s. 1369-1384 Tidskriftsartikel (refereegranskat)abstract A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in this paper we address some of these issues. In particular, we derive existence and uniqueness results for the Black-Scholes equation, and we provide convexity theory for option pricing and derive related ordering results with respect to volatility. We show that American options are convexity preserving, whereas European options preserve concavity for general payoffs and convexity only for bounded contracts.
22.	Ekström, Erik, 1977-, et al. (författare) De Finetti's Control Problem with Competition 2023 Ingår i: Applied mathematics and optimization. - : Springer Science and Business Media LLC. - 0095-4616 .- 1432-0606. ; 87:2 Tidskriftsartikel (refereegranskat)abstract We investigate the effects of competition in a problem of resource extraction from a common source with diffusive dynamics. In the symmetric version with identical extraction rates we provide conditions for the existence of a Nash equilibrium where the strategies are of threshold type, and we characterize the equilibrium threshold. Moreover, we show that increased competition leads to lower extraction thresholds and smaller equilibrium values. For the asymmetric version, where each agent has an individual extraction rate, we provide the existence of an equilibrium in threshold strategies, and we show that the corresponding thresholds are ordered in the same way as the extraction rates.
23.	Ekström, Erik, 1977-, et al. (författare) Dupire's equation for bubbles Annan publikation (övrigt vetenskapligt/konstnärligt)
24.	Ekström, Erik, 1977-, et al. (författare) Dynkin Games With Heterogeneous Beliefs 2017 Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 54:1, s. 236-251 Tidskriftsartikel (refereegranskat)abstract We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions, then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.
25.	Ekström, Erik, 1977-, et al. (författare) Dynkin ghost games with asymmetry and consolation Annan publikation (övrigt vetenskapligt/konstnärligt)
26.	Ekström, Erik, 1989-, et al. (författare) Epitaxial Growth of CaMnO3–y Films on LaAlO3 (11‾20) by Pulsed Direct Current Reactive Magnetron Sputtering 2022 Ingår i: Physica Status Solidi. Rapid Research Letters. - : Wiley-VCH Verlagsgesellschaft. - 1862-6254 .- 1862-6270. ; 16:4 Tidskriftsartikel (refereegranskat)abstract CaMnO3 is a perovskite with attractive magnetic and thermoelectric properties. CaMnO3 films are usually grown by pulsed laser deposition or radio frequency magnetron sputtering from ceramic targets. Herein, epitaxial growth of CaMnO3–y (002) films on a (11‾20)-oriented LaAlO3 substrate using pulsed direct current reactive magnetron sputtering is demonstrated, which is more suitable for industrial scale depositions. The CaMnO3–y shows growth with a small in-plane tilt of <≈0.2° toward the (200) plane of CaMnO3–y and the (1‾104) with respect to the LaAlO3 (11‾20) substrate. X-ray photoelectron spectroscopy of the electronic core levels shows an oxygen deficiency described by CaMnO2.58 that yields a lower Seebeck coefficient and a higher electrical resistivity when compared to stoichiometric CaMnO3. The LaAlO3 (11‾20) substrate promotes tensile-strained growth of single crystals. Scanning transmission electron microscopy and electron energy loss spectroscopy reveal antiphase boundaries composed of Ca on Mn sites along <101> and <002>, forming stacking faults.
27.	Ekström, Erik, 1989- (författare) Epitaxial growth, structure, and thermoelectric properties of CaMn- and V-based oxides 2021 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract This thesis is focused on physical vapor deposition, epitaxy, and structural characterization of CaMnO3 and VO2. Environmentally friendly and abundant materials are important for energy savings in applications, e.g., thermoelectrics for waste-heat recycling and thermochromic materials for passive indoor-temperature regulation. CaMnO3 is thermoelectric and VO2 is thermochromic at attractive temperatures for waste heat recycling and passive indoor-temperature regulation, respectively. The two material systems in this thesis were grown by reactive magnetron sputtering. A two-step synthesis process was investigated where rock-salt (Ca,Mn)O was grown by sputtering followed by an annealing step to form the perovskite CaMnO3. CaMnO3 was alloyed with Nb with the purpose to enhance the thermoelectric properties by increasing the number of free carriers, resulting in CaMn1-xNbxO3 (x = 0 – 0.10) films. CaMnO3 was grown on Al2O3 and LaAlO3 while VO2 was grown on muscovite (mica), phase-pure films of the metastable B phase and the stable M1 phase could be grown by controlling the gas flow and pressure. The mica substrate is a material with weakly interacting van der Waals layers in the structure that enable van der Waals epitaxy for the stable VO2 film in M1 phase. The thickness effect on electrical properties in the thermochromic region was investigated as well as proving van der Waals epitaxy. This thesis therefore provides an overall contribution to the understanding of film structure and the control thereof and how it affects the properties of the film.
28.	Ekström, Erik, 1977-, et al. (författare) How To Detect A Salami Slicer : A Stochastic Controller-And-Stopper Game With Unknown Competition 2022 Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics Publications. - 0363-0129 .- 1095-7138. ; 60:1, s. 545-574 Tidskriftsartikel (refereegranskat)abstract We consider a stochastic game of control and stopping specified in terms of a process $X_t=-\theta \Lambda_t+W_t$, representing the holdings of Player 1, where $W$ is a Brownian motion, $\theta$ is a Bernoulli random variable indicating whether Player 2 is active or not, and $\Lambda$ is a nondecreasing continuous process representing the accumulated "theft" or "fraud" performed by Player 2 (if active) against Player 1. Player 1 cannot observe $\theta$ or $\Lambda$ directly but can merely observe the path of the process $X$ and may choose a stopping rule $\tau$ to deactivate Player 2 at a cost $M$. Player 1 thus does not know if she is the victim of fraud or not and operates in this sense under unknown competition. Player 2 can observe both $\theta$ and $W$ and seeks to choose a fraud strategy $\Lambda$ that maximizes the expected discounted amount ${\mathbb E} \left [ \left. \int _0^{\tau} e^{-rs} d\Lambda_s \right \vert \theta=1\right ],$ whereas Player 1 seeks to choose the stopping strategy $\tau$ so as to minimize the expected discounted cost ${\mathbb E} \left [\theta \int _0^{\tau} e^{-rs} d\Lambda_s + e^{-r\tau}M\I{\tau<\infty} \right ].$ This non-zero-sum game belongs to a class of stochastic dynamic games with unknown competition and continuous controls and is motivated by applications in fraud detection; it combines filtering (detection), stochastic control, optimal stopping, strategic features (games), and asymmetric information. We derive Nash equilibria for this game; for some parameter values we find an equilibrium in pure strategies, and for other parameter values we find an equilibrium by allowing for randomized stopping strategies.
29.	Ekström, Erik, 1977-, et al. (författare) Monotonicity of implied volatility for perpetual put options 2024 Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 61:1, s. 301-310 Tidskriftsartikel (refereegranskat)abstract We define and study properties of implied volatility for American perpetual put options. In particular, we show that if the market prices are derived from a local volatility model with a monotone volatility function, then the corresponding implied volatility is also monotone as a function of the strike price.
30.	Ekström, Erik, 1977-, et al. (författare) Multi-dimensional sequential testing and detection 2022 Ingår i: Stochastics. - : Taylor & Francis. - 1744-2508 .- 1744-2516. ; 94:5, s. 789-806 Tidskriftsartikel (refereegranskat)abstract We study extensions to higher dimensions of the classical Bayesian sequen- tial testing and detection problems for Brownian motion. In the main result we show that, for a large class of problem formulations, the cost function is unilaterally concave. This concavity result is then used to deduce structural properties for the continuation and stopping regions in specific examples.
31.	Ekström, Erik, 1977-, et al. (författare) Optimal liquidation of a pairs trade Annan publikation (populärvet., debatt m.m.)
32.	Ekström, Erik, 1977-, et al. (författare) Optimal selling of an asset under incomplete information 2011 Ingår i: International Journal of Stochastic Analysis. - : Hindawi Limited. - 2090-3332 .- 2090-3340. ; 2011, s. 543590- Tidskriftsartikel (refereegranskat)abstract We consider an agent who wants to liquidate an asset with unknown drift. The agent believes that the drift takes one of two given values and has initially an estimate for the probability of either of them. As time goes by, the agent observes the asset price and can thereforeupdate his beliefs about the probabilities for the drift distribution. We formulate an optimal stopping problem that describes the liquidation problem, and we demonstrate that the optimal strategy is to liquidate the first time the asset price falls below a certain time-dependent boundary. Moreover, this boundary is shown to be monotonically increasing, continuous and to satisfy a nonlinear integral equation.
33.	Ekström, Erik, 1977-, et al. (författare) Optimal stopping games for Markov processes 2008 Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 47:2, s. 684-702 Tidskriftsartikel (refereegranskat)
34.	Ekström, Erik, 1977-, et al. (författare) Optimal stopping of a Brownian bridge with an unknown pinning point 2020 Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149 .- 1879-209X. ; 130:2, s. 806-823 Tidskriftsartikel (refereegranskat)abstract The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established. However, structural properties of the optimal stopping region are shown to crucially depend on the prior, and we provide a general condition for a one-sided stopping region. Moreover, a detailed analysis is conducted in the cases of the two-point and the mixed Gaussian priors, revealing a rich structure present in the problem.
35.	Ekström, Erik, 1977- (författare) Selected Problems in Financial Mathematics 2004 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract This thesis, consisting of six papers and a summary, studies the area of continuous time financial mathematics. A unifying theme for many of the problems studied is the implications of possible mis-specifications of models. Intimately connected with this question is, perhaps surprisingly, convexity properties of option prices. We also study qualitative behavior of different optimal stopping boundaries appearing in option pricing.In Paper I a new condition on the contract function of an American option is provided under which the option price increases monotonically in the volatility. It is also shown that American option prices are continuous in the volatility.In Paper II an explicit pricing formula for the perpetual American put option in the Constant Elasticity of Variance model is derived. Moreover, different properties of this price are studied.Paper III deals with the Russian option with a finite time horizon. It is shown that the value of the Russian option solves a certain free boundary problem. This information is used to analyze the optimal stopping boundary.A study of perpetual game options is performed in Paper IV. One of the main results provides a condition under which the value of the option is increasing in the volatility.In Paper V options written on several underlying assets are considered. It is shown that, within a large class of models, the only model for the stock prices that assigns convex option prices to all convex contract functions is geometric Brownian motion.Finally, in Paper VI it is shown that the optimal stopping boundary for the American put option is convex in the standard Black-Scholes model.
36.	Ekström, Erik, 1977-, et al. (författare) Stopping problems with an unknown state 2023 Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. Tidskriftsartikel (refereegranskat)
37.	Ekström, Erik, 1977-, et al. (författare) The de Finetti problem with uncertain competition 2023 Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 61:5, s. 2997-3017 Tidskriftsartikel (refereegranskat)abstract We consider a resource extraction problem which extends the classical de Finetti problem for a Wiener process to include the case when a competitor, who is equipped with the ability to extract all the remaining resources in one piece, may exist. This situation is modeled as a nonzero-sum controller-and-stopper game with incomplete information. For this stochastic game we provide a Nash equilibrium with an explicit structure. In equilibrium, the agent and the competitor use singular strategies in such a way that a two-dimensional process, which represents available resources and the filtering estimate of active competition, reflects in a specific direction along a given boundary.
38.	Ekström, Sven-Erik, 1977- (författare) Matrix-Less Methods for Computing Eigenvalues of Large Structured Matrices 2018 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract When modeling natural phenomena with linear partial differential equations, the discretized system of equations is in general represented by a matrix. To solve or analyze these systems, we are often interested in the spectral behavior of these matrices. Whenever the matrices of interest are Toeplitz, or Toeplitz-like, we can use the theory of Generalized Locally Toeplitz (GLT) sequences to study the spectrum (eigenvalues). A central concept in the theory of GLT sequences is the so-called symbol, that is, a function associated with a sequence of matrices of increasing size. When sampling the symbol and when the related matrix sequence is Hermitian (or quasi-Hermitian), we obtain an approximation of the spectrum of a matrix of a fixed size and we can therefore see its general behavior. However, the so-computed approximations of the eigenvalues are often affected by errors having magnitude of the reciprocal of the matrix size.In this thesis we develop novel methods, which we call "matrix-less" since they neither store the matrices of interest nor depend on matrix-vector products, to estimate these errors. Moreover, we exploit the structures of the considered matrices to efficiently and accurately compute the spectrum.We begin by considering the errors of the approximate eigenvalues computed by sampling the symbol on a uniform grid, and we conjecture the existence of an asymptotic expansion for these errors. We devise an algorithm to approximate the expansion by using a small number of moderately sized matrices, and we show through numerical experiments the effectiveness of the algorithm. We also show that the same algorithm works for preconditioned matrices, a result which is important in practical applications. Then, we explain how to use the approximated expansion on the whole spectrum for large matrices, whereas in earlier works its applicability was restricted only to certain matrix sizes and to a subset of the spectrum. Next, we demonstrate how to use the so-developed techniques to investigate, solve, and improve the accuracy in the eigenvalue computations for various differential problems discretized by the isogeometric analysis (IgA) method. Lastly, we discuss a class of non-monotone symbols for which we construct the sampling grid yielding exact eigenvalues and eigenvectors.To summarize, we show, both theoretically and numerically, the applicability of the presented matrix-less methods for a wide variety of problems.
39.	Landälv, Ludvig, 1982-, et al. (författare) Phase evolution of radio frequency magnetron sputtered Cr-rich (Cr,Zr)(2)O-3 coatings studied by in situ synchrotron X-ray diffraction during annealing in air or vacuum 2019 Ingår i: Journal of Materials Research. - : CAMBRIDGE UNIV PRESS. - 0884-2914 .- 2044-5326. ; 34:22, s. 3735-3746 Tidskriftsartikel (refereegranskat)abstract The phase evolution of reactive radio frequency (RF) magnetron sputtered Cr0.28Zr0.10O0.61 coatings has been studied by in situ synchrotron X-ray diffraction during annealing under air atmosphere and vacuum. The annealing in vacuum shows t-ZrO2 formation starting at similar to 750-800 degrees C, followed by decomposition of the alpha-Cr2O3 structure in conjunction with bcc-Cr formation, starting at similar to 950 degrees C. The resulting coating after annealing to 1140 degrees C is a mixture of t-ZrO2, m-ZrO2, and bcc-Cr. The air-annealed sample shows t-ZrO2 formation starting at similar to 750 degrees C. The resulting coating after annealing to 975 degrees C is a mixture of t-ZrO2 and alpha-Cr2O3 (with dissolved Zr). The microstructure coarsened slightly during annealing, but the mechanical properties are maintained, with no detectable bcc-Cr formation. A larger t-ZrO2 fraction compared with alpha-Cr2O3 is observed in the vacuum-annealed coating compared with the air-annealed coating at 975 degrees C. The results indicate that the studied pseudo-binary oxide is more stable in air atmosphere than in vacuum.
40.	Lundgren, Robin, 1977- (författare) Optimal Stopping and Convergence of Option Rewards 2009 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract This thesis is based on two articles devoted to optimal stopping problems of American type options. In article A, we study the problem of optimal reselling for European options. The problem can be transformed to the problem of exercising an American option with two underlying. An approximate binomial-trinomial tree algorithm for the reselling model is constructed. In article B, we get general convergence results for the American option rewards for multivariate Markov price processes. These results are used to prove convergence of tree approximations presented in papers A and B.
41.	Wang, Yuqiong (författare) Optimal stopping, incomplete information, and stochastic games 2023 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract This thesis contains six papers on the topics of optimal stopping and stochastic games. Paper I extends the classical Bayesian sequential testing and detection problems for a Brownian motion to higher dimensions. We demonstrate unilateral concavity of the cost function and present its structural properties through various examples.Paper II studies the problem of sequentially testing two composite hypotheses concerning an unknown parameter within the exponential family, incorporating observation costs within the Bayesian setting. In a Markovian framework, we show that the value function is concave, and non-decreasing in time under certain assumptions, consequently leading to the monotonicity of the stopping boundaries.Paper III formulates an optimal stopping problem involving an unknown state that influences the diffusion process drift, the payoff functions, and the distribution of the time horizon. By performing a measure change, we reformulate it into a two-dimensional stopping problem with full information. We further provide several examples where explicit solutions are possible.Paper IV introduces some non-linear, non-local parabolic operators related to a tug-of-war game where the random waiting time is coupled with space. Following that, we state and prove the asymptotic mean value formulas of the fractional heat operator and the aforementioned operators, and discuss their probabilistic interpretations. Paper V considers a Dynkin game with consolation where the players act under asymmetric and incomplete information. We prove a verification result that allows us to identify a Nash equilibrium. Building upon this, we examine certain classes of problems where the equilibrium value functions and strategies can be constructed.Paper VI addresses the Bayesian sequential estimation problem of an unknown parameter within the exponential family, considering observations with associated costs. We offer sufficient conditions for space monotonicity of the value function, and explore their consequential impacts on the structural attributes of continuation and stopping regions.
42.	Wang, Yuqiong (författare) Structural properties of problems in sequential testing and detection 2021 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)
43.	Zena, Lucas, 1984, et al. (författare) Beating the heart failure odds: long-term survival after myocardial ischemia in juvenile rainbow trout 2024 Ingår i: AMERICAN JOURNAL OF PHYSIOLOGY-REGULATORY, INTEGRATIVE AND COMPARATIVE PHYSIOLOGY. - 0363-6119 .- 1522-1490. ; 326:6 Tidskriftsartikel (refereegranskat)abstract Salmonid fish include some of the most valued cultured fish species worldwide. Unlike most other fish, the hearts of salmonids, including Atlantic salmon and rainbow trout, have a well-developed coronary circulation. Consequently, their hearts' reliance on oxygenation through coronary arteries leaves them prone to coronary lesions, believed to precipitate myocardial ischemia. Here, we mimicked such coronary lesions by subjecting groups of juvenile rainbow trout to coronary ligation, assessing histomorphological myocardial changes associated with ischemia and scarring in the context of cardiac arrhythmias using electrocardiography (ECG). Notable ECG changes resembling myocardial ischemia-like ECG in humans, such as atrioventricular blocks and abnormal ventricular depolarization (prolonged and fragmented QRS complex), as well as repolarization (long QT interval) patterns, were observed during the acute phase of myocardial ischemia. A remarkable 100% survival rate was observed among juvenile trout subjected to coronary ligation after 24 wk. Recovery from coronary ligation occurred through adaptive ventricular remodeling, coupled with a fast cardiac revascularization response. These findings carry significant implications for understanding the mechanisms governing cardiac health in salmonid fish, a family particularly susceptible to cardiac diseases. Furthermore, our results provide valuable insights into comparative studies on the evolution, pathophysiology, and ontogeny of vertebrate cardiac repair and restoration. NEW & NOTEWORTHY Juvenile rainbow trout exhibit a remarkable capacity to recover from cardiac injury caused by myocardial ischemia. Recovery from cardiac damage occurs through adaptive ventricular remodeling, coupled with a rapid cardiac revascularization response. These findings carry significant implications for understanding the mechanisms governing cardiac health within salmonid fishes, which are particularly susceptible to cardiac diseases.

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