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Sökning: WFRF:(Christensen Sören 1982)

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1.
  • Christensen, Björn, et al. (författare)
  • Achtung: Statistik. 150 Kolumnen zum Nachdenken und Schmunzeln
  • 2015
  • Bok (övrigt vetenskapligt/konstnärligt)abstract
    • Mit 150 Kolumnen „Achtung Statistik“ bietet das Buch eine kurzweilige Möglichkeit, Statistik zukünftig mit anderen Augen zu sehen, kritisch zu hinterfragen und in Einzelfällen sogar wissenschaftliche Top-Nachrichten mit gesundem Menschenverstand als statistische „Rohrkrepierer“ zu entlarven. Geprägt durch den Spruch: „Trau keiner Statistik, die du nicht selbst gefälscht hast!“ hat die Statistik wirklich keinen guten Ruf. Sie gilt als eine trockene, schwierige Materie, die uns zwar auf Schritt und Tritt in Schule, Studium und Beruf, aber auch in den Medien begegnet, zu der die meisten aber kaum Zugang finden. Die Autoren zeigen, dass es möglich ist, ohne besondere Vorbildung und mit einem Schmunzeln interessante und erstaunliche statistische Erkenntnisse zu gewinnen, zu deren Verständnis keine Formeln nötig sind. Die seit 2012 regelmäßig im „Schleswig-Holstein Journal“ publizierten Kolumnen wurden für das Buch um weitergehende Erläuterungen und Beispiele ergänzt.
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2.
  • Christensen, B., et al. (författare)
  • Are female hurricanes really deadlier than male hurricanes?
  • 2014
  • Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 111:34, s. E3497-E3498
  • Tidskriftsartikel (refereegranskat)
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3.
  • Christensen, B., et al. (författare)
  • Discrimination of mothers for convalescent treatment? | Diskriminierung bei Kuren für Mütter?
  • 2015
  • Ingår i: Pravention und Gesundheitsforderung. - : Springer Science and Business Media LLC. - 1861-6755 .- 1861-6763. ; 10:3, s. 218-221
  • Tidskriftsartikel (refereegranskat)abstract
    • © 2015 Springer-Verlag Berlin Heidelberg Background: In the data report 2014, the German Maternal Convalescence Movement (Müttergenesungswerk) identified a possible discrimination against mothers with a low level of education in health convalescent treatment allocation. Objective: The question whether this discrimination is supported by data is investigated. Material and methods: Based on a special analysis of the microcensus (Statistisches Bundesamt), the percentage of the education level of all economically active mothers with a child under the age of 10 years is compared with the corresponding percentages of health convalescent treatment participants. Results: No discrimination against mothers with a low level of education in health convalescent treatment allocation was found in this data set.
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4.
  • Christensen, Björn, et al. (författare)
  • Everything counts!
  • 2015
  • Ingår i: AStA Wirtschafts- und Sozialstatistisches Archiv. - : Springer Science and Business Media LLC. - 1863-8155 .- 1863-8163. ; 9:3-4, s. 215-232
  • Tidskriftsartikel (refereegranskat)abstract
    • Mit der Durchführung des Zensus 2011 ist die Bundesrepublik Deutschland ihrer Verpflichtung aus der EU-Verordnung 763/2008 vom 9. Juli 2008, eine Volkszählung nach festgelegten Kriterien durchzuführen, nachgekommen. Im Gegensatz zu früheren Volkszählungen (1987 BRD und 1981 DDR) wurde beim Zensus 2011 nicht auf eine Vollerhebung zurückgegriffen, sondern ein registergestütztes Verfahren verwendet. Für die Gemeinden stehen, durch die Veröffentlichung der Ergebnisse am 31.05.2013, unter anderem die amtlichen Bevölkerungszahlen zur Verfügung. Der Groß teil der Gemeinden sieht sich elementaren Verringerungen innerhalb ihres Einwohnerbestands gegenüber. Dieses Papier zeigt auf, dass Gemeinden unterhalb von 10.000 Einwohner signifikant geringere relative Verluste in den Einwohnerzahlen durch den Zensus 2011 im Vergleich zu Gemeinden mit mehr als 10.000 Einwohner aufweisen.
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5.
  • Christensen, Björn, et al. (författare)
  • Everything counts! : Warum kleine Gemeinden die Gewinner der Zensuserhebung 2011 sind
  • 2015
  • Ingår i: AStA Wirtschafts- und Sozialstatistisches Archiv. - : Springer Science and Business Media LLC. - 1863-8155 .- 1863-8163. ; 9:3-4, s. 215-232
  • Tidskriftsartikel (refereegranskat)abstract
    • Mit der Durchführung des Zensus 2011 ist die Bundesrepublik Deutschland ihrer Verpflichtung aus der EU-Verordnung 763/2008 vom 9. Juli 2008, eine Volkszählung nach festgelegten Kriterien durchzuführen, nachgekommen. Im Gegensatz zu früheren Volkszählungen (1987 BRD und 1981 DDR) wurde beim Zensus 2011 nicht auf eine Vollerhebung zurückgegriffen, sondern ein registergestütztes Verfahren verwendet. Für die Gemeinden stehen, durch die Veröffentlichung der Ergebnisse am 31.05.2013, unter anderem die amtlichen Bevölkerungszahlen zur Verfügung. Der Groß teil der Gemeinden sieht sich elementaren Verringerungen innerhalb ihres Einwohnerbestands gegenüber. Dieses Papier zeigt auf, dass Gemeinden unterhalb von 10.000 Einwohner signifikant geringere relative Verluste in den Einwohnerzahlen durch den Zensus 2011 im Vergleich zu Gemeinden mit mehr als 10.000 Einwohner aufweisen.
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6.
  • Belak, C., et al. (författare)
  • Worst-case optimal investment with a random number of crashes
  • 2014
  • Ingår i: Statistics and Probability Letters. - : Elsevier BV. - 0167-7152. ; 90:1, s. 140-148
  • Tidskriftsartikel (refereegranskat)abstract
    • We study a portfolio optimization problem in a market which is under the threat of crashes. At random times, the investor receives a warning that a crash in the risky asset might occur. We construct a strategy which renders the investor indifferent about an immediate crash of maximum size and no crash at all. We then verify that this strategy outperforms every other trading strategy using a direct comparison approach. We conclude with numerical examples and calculating the costs of hedging against crashes. © 2014 Elsevier B.V.
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7.
  • Belak, Christoph, et al. (författare)
  • Worst-case portfolio optimization in a market with bubbles
  • 2016
  • Ingår i: International Journal of Theoretical and Applied Finance. - 0219-0249. ; 19:2
  • Tidskriftsartikel (refereegranskat)abstract
    • We investigate a utility maximization problem in the presence of asset price bubbles. At random times, the investor receives warnings that a bubble has formed in the market which may lead to a crash in the risky asset. We propose a regime-switching model for the warnings and we make no assumptions about the distribution of the timing and the size of the crashes. Instead, we assume that the investor takes a worst-case perspective towards their impacts, i.e. the investor maximizes her expected utility under the worst-case crash scenario. We characterize the value function by a system of Hamilton–Jacobi–Bellman equations and derive a coupled system of ordinary differential equations for the optimal strategies. Numerical examples are provided.
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8.
  • Christensen, Sören, 1982, et al. (författare)
  • A harmonic function technique for the optimal stopping of diffusions
  • 2011
  • Ingår i: Stochastics. - : Informa UK Limited. - 1744-2508 .- 1744-2516. ; 83:4-6, s. 347-363
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider problems of optimal stopping where the driving process is a (one- or multi-dimensional) diffusion. Our approach is motivated by a change of measure techniques and gives a characterization of the optimal stopping set in terms of harmonic functions for one-dimensional diffusions. The generalization to multidimensional diffusions uses the theory of Martin boundaries. Various applications, including exchange options, are given. We treat an example where halfspaces, which are plausible candidates for the optimal stopping set, are in fact strict subsets of it. © 2011 Copyright Taylor and Francis Group, LLC.
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9.
  • Christensen, Sören, 1982 (författare)
  • A method for pricing american options using semi-infinite linear programming
  • 2014
  • Ingår i: Mathematical Finance. - : Wiley. - 1467-9965 .- 0960-1627. ; 24:1, s. 156-172
  • Tidskriftsartikel (refereegranskat)abstract
    • We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these functions. The resulting problem is a linear semi-infinite programming problem, that can be solved using standard algorithms. This leads to good upper bounds for the original problem. For our algorithms no discretization of space and time and no simulation is necessary. Furthermore it is applicable even for high-dimensional problems. The algorithm provides an approximation of the value not only for one starting point, but for the complete value function on the continuation set, so that the optimal exercise region and, for example, the Greeks can be calculated. We apply the algorithm to (one- and) multidimensional diffusions and show it to be fast and accurate. © 2012 Wiley Periodicals, Inc.
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10.
  • Christensen, Sören, 1982, et al. (författare)
  • A note on pasting conditions for the American perpetual optimal stopping problem
  • 2009
  • Ingår i: Statistics and Probability Letters. - : Elsevier BV. - 0167-7152. ; 79:3, s. 349-353
  • Tidskriftsartikel (refereegranskat)abstract
    • The principles of smooth and continuous pasting play an important role in the study of optimal stopping problems with jump processes. These principles state that the optimal stopping boundary is selected so that the value function is smooth and continuous, respectively (depending on the behavior of the underlying process at the boundary). Extending the results of Alili & Kyprianou [Alili, L., Kyprianou, A.E., 2005. Some remarks on first passage of Lévy processes, the American put and pasting principles. Ann. Appl. Probab. 15, 2062-2080] we show that in the case of an American perpetual put under a Lévy process the optimal stopping point is in fact characterized as the only point that fulfills this smooth/continuous pasting condition. © 2008 Elsevier B.V. All rights reserved.
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11.
  • Christensen, Sören, 1982, et al. (författare)
  • American Options with guarantee – A class of two-sided stopping problems
  • 2013
  • Ingår i: Statistics and Risk Modeling. - 2193-1402 .- 2196-7040. ; 30:3, s. 237-254
  • Tidskriftsartikel (refereegranskat)abstract
    • We introduce a class of optimal stopping problems in which the gain is at least a fraction of the initial value. From a financial point of view this structure can be seen as a guarantee for the holder of an American option. It turns out that the optimal strategies are of two-sided type under weak conditions. If the driving process is a diffusion we use harmonic-functions techniques to obtain general results. For an explicit solution we derive two differential equations that characterize the optimal strategies. Furthermore we study the case of Lévy processes. An explicit solution is obtained for spectrally negative processes using scale functions
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12.
  • Christensen, Sören, 1982 (författare)
  • An effective method for the explicit solution of sequential problems on the real line
  • 2017
  • Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 36:1, s. 2-18
  • Tidskriftsartikel (refereegranskat)abstract
    • A general method for solving optimal stopping problems for continuous-time Markov processes on the real line is developed. The basic idea is to first study an auxiliary problem for the two-dimensional process consisting of the underlying Markov process and its running maximum. It turns out that this auxiliary problem is much easier to solve using standard methods such as the monotonicity of the problem, and an optimal strategy in the class of threshold times can be found. The optimality of the time carries over to original problem. This two-step procedure gives a unifying approach for solving problems from different fields such as mathematical finance and sequential analysis. © 2017 Taylor & Francis.
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13.
  • Christensen, Sören, 1982, et al. (författare)
  • An elementary approach to optimal stopping problems for AR(1) sequences
  • 2011
  • Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 30:1, s. 79-93
  • Tidskriftsartikel (refereegranskat)abstract
    • Optimal stopping problems form a class of stochastic optimization problems that has a wide range of applications in sequential statistics and mathematical finance. Here we consider a general optimal stopping problem with discounting for autoregressive processes. Our strategy for a solution consists of two steps: First we give elementary conditions to ensure that an optimal stopping time is of threshold type. Then the resulting one-dimensional problem of finding the optimal threshold is to be solved explicitly. The second step is carried out for the case of exponentially distributed innovations. © Taylor & Francis Group, LLC.
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14.
  • Christensen, Sören, 1982, et al. (författare)
  • Classification error in multiclass discrimination from Markov data
  • 2015
  • Ingår i: Statistical Inference for Stochastic Processes. - : Springer Science and Business Media LLC. - 1387-0874 .- 1572-9311. ; 19:3, s. 321-336
  • Tidskriftsartikel (refereegranskat)abstract
    • © 2015 Springer Science+Business Media Dordrecht As a model for an on-line classification setting we consider a stochastic process (Formula presented.), the present time-point being denoted by 0, with observables (Formula presented.) from which the pattern (Formula presented.) is to be inferred. So in this classification setting, in addition to the present observation (Formula presented.) a number l of preceding observations may be used for classification, thus taking a possible dependence structure into account as it occurs e.g. in an ongoing classification of handwritten characters. We treat the question how the performance of classifiers is improved by using such additional information. For our analysis, a hidden Markov model is used. Letting (Formula presented.) denote the minimal risk of misclassification using l preceding observations we show that the difference (Formula presented.) decreases exponentially fast as l increases. This suggests that a small l might already lead to a noticeable improvement. To follow this point we look at the use of past observations for kernel classification rules. Our practical findings in simulated hidden Markov models and in the classification of handwritten characters indicate that using (Formula presented.), i.e. just the last preceding observation in addition to (Formula presented.), can lead to a substantial reduction of the risk of misclassification. So, in the presence of stochastic dependencies, we advocate to use (Formula presented.) for finding the pattern (Formula presented.) instead of only (Formula presented.) as one would in the independent situation.
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15.
  • Christensen, Sören, 1982 (författare)
  • Contributions to the theory of optimal stopping
  • 2010
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis deals with the explicit solution of optimal stopping problems with infinite time horizon. To solve Markovian problems in continuous time we introduce an approach that gives rise to explicit results in various situations. The main idea is to characterize the optimal stopping set as the union of the maximum points of explicitly given functions involving the harmonic functions for the underlying stochastic process. This provides elementary solutions for a variety of optimal stopping problems and answers questions concerning the geometric shape of the optimal stopping set. The approach is shown to work well for one- and multidimensional diffusion processes, spectrally negative Lévy processes and problems containing the running maxima process. Furthermore we introduce a new class of problems, which we call problems with guarantee. For continuous one-dimensional driving processes and certain Lévy processes we prove that the optimal strategies are of two-sided type and establish first-order ODEs that characterize the solution. In the second part we consider optimal stopping problems for autoregressive processes in discrete time. This class of processes is intensively studied in statistics and other fields of applied probability. We establish elementary conditions to ensure that the optimal stopping time is of threshold type and find the joint distribution of the threshold-time and the overshoot for a wide class of innovations. Using the principle of continuous fit this leads to explicit solutions.
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16.
  • Christensen, Sören, 1982, et al. (författare)
  • Convergence of switching diffusions
  • 2015
  • Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 125:9, s. 3623-3635
  • Tidskriftsartikel (refereegranskat)abstract
    • © 2015 Elsevier B.V. This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on semimartingale techniques, so that no Markovian assumption for the modulating process is needed.
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17.
  • Christensen, Sören, 1982 (författare)
  • Discussion on "Sequential Estimation for Time Series Models" by T. N. Sriram and Ross Iaci
  • 2014
  • Ingår i: Sequential Analysis. - : Informa UK Limited. - 1532-4176 .- 0747-4946. ; 33:2, s. 158-160
  • Tidskriftsartikel (refereegranskat)abstract
    • Based on the excellent review and numerical study presented by Professor T. N. Sriram and Professor R. Iaci, another sequential problem for autoregressive processes is discussed. © 2014 Copyright Taylor & Francis Group, LLC.
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18.
  • Christensen, Sören, 1982 (författare)
  • Generalized Fibonacci numbers and Blackwell's renewal theorem
  • 2012
  • Ingår i: Statistics and Probability Letters. - : Elsevier BV. - 0167-7152. ; 82:9, s. 1665-1668
  • Tidskriftsartikel (refereegranskat)abstract
    • We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation. © 2012 Elsevier B.V.
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19.
  • Christensen, Sören, 1982, et al. (författare)
  • IMPULSE CONTROL AND EXPECTED SUPREMA
  • 2017
  • Ingår i: Advances in Applied Probability. - : Cambridge University Press (CUP). - 0001-8678 .- 1475-6064. ; 49:1, s. 238-257
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider a class of impulse control problems for general underlying strong Markov processes on the real line, which allows for an explicit solution. The optimal impulse times are shown to be of a threshold type and the optimal threshold is characterised as a solution of a (typically nonlinear) equation. The main ingredient we use is a representation result for excessive functions in terms of expected suprema.
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20.
  • Christensen, Sören, 1982 (författare)
  • No Benefit in Seeing a Dark Future? On Recent Findings on the Effects of Forecasting Life Satisfaction
  • 2016
  • Ingår i: Journal of Individual Differences. - : Hogrefe Publishing Group. - 1614-0001 .- 2151-2299. ; 37:3, s. 201-2015
  • Tidskriftsartikel (refereegranskat)abstract
    • In their article, Lang, Weiss, Gerstorf, & Wagner, (2013) use the adult life span sample of the national German Socio-Economic Panel (GSOEP) to explore functional outcomes of life satisfaction with regard to hazards of mortality. Their findings suggest that "being overly optimistic [in] predicting a better future than actually observed was associated with [...] a great risk of mortality within the following decade." In this short paper, we analyze the same data set using the same model, but, in addition to the self-rated health status in the starting year included in the model by Lang et al. (2013), we furthermore control for the self-rated health at the target year. With this modification, it turns out that the accuracy of anticipated future life satisfaction has no significant effect on mortality. Two additional analyses underpin this finding.
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21.
  • Christensen, Sören, 1982 (författare)
  • On sequential decision problems with constant costs of observation
  • 2016
  • Ingår i: Stochastic Processes and Models in Operations Research. Neelamegam Anbazhagan (red.). - : IGI. - 9781522500445
  • Bokkapitel (refereegranskat)abstract
    • We present a solution technique for optimal stopping problems with constant costs of observation in a diffusion setting. Such problems arise naturally, e.g., in Wald's type sequential decision problems and the Portfolio optimization model by Morton and Pliska. The main result is that the treatment of such problem boils down to the determination of the maximum points of a class of explicitly given functions. The findings are illustrated by a variety of examples and generalized to random costs of observation.
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22.
  • Christensen, Sören, 1982 (författare)
  • On Stochastic Control and Optimal Stopping in Continuous Time
  • 2013
  • Bok (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis deals with the solution of optimal stopping- and more general stochastic control problems for continuous time Markov processes. The focus lies on introducing new effective methods for solving different classes of problems explicitly.
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23.
  • Christensen, Sören, 1982 (författare)
  • On the Distribution of Random Variables Corresponding to Musielak-Orlicz Norms
  • 2013
  • Ingår i: Studia Mathematica. - 1730-6337 .- 0039-3223. ; 219:3, s. 269-287
  • Tidskriftsartikel (refereegranskat)abstract
    • Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X1,…,Xn are independent copies of X, then1Cp∥x∥M≤?∥(xiXi)ni=1∥p≤Cp∥x∥M,where Cp is a positive constant depending only on p. In case p=2 we need the function t↦tM′(t)−M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L1[0,1]. We also provide a general result replacing the ℓp-norm by an arbitrary N-norm. This complements some deep results obtained by Gordon, Litvak, Schütt, and Werner [Ann. Prob. 30 (2002)]. We also prove, in the spirit of that paper, a result which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak–Orlicz spaces.
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24.
  • Christensen, Sören, 1982 (författare)
  • On the solution of general impulse control problems using superharmonic functions
  • 2014
  • Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 124:1, s. 709-729
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, a characterization of the solution of impulse control problems in terms of superharmonic functions is given. In a general Markovian framework, the value function of the impulse control problem is shown to be the minimal function in a convex set of superharmonic functions. This characterization also leads to optimal impulse control strategies and can be seen as the corresponding characterization to the description of the value function for optimal stopping problems as a smallest superharmonic majorant of the reward function. The results are illustrated with examples from different fields, including multiple stopping and optimal switching problems. © 2013 Elsevier B.V. All rights reserved.
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25.
  • Christensen, Sören, 1982 (författare)
  • Optimal decision under ambiguity for diffusion processes
  • 2013
  • Ingår i: Mathematical Methods of Operations Research. - : Springer Science and Business Media LLC. - 1432-2994 .- 1432-5217. ; 77:2, s. 207-226
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed. © 2013 Springer-Verlag Berlin Heidelberg.
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26.
  • Christensen, Sören, 1982, et al. (författare)
  • Optimal Multiple Stopping with Random Waiting Times
  • 2013
  • Ingår i: Sequential Analysis. - : Informa UK Limited. - 1532-4176 .- 0747-4946. ; 32:3, s. 297-318
  • Tidskriftsartikel (refereegranskat)abstract
    • In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length δ, the so-called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise case. In this article we generalize the standard model by considering random refraction times. We develop the theory and reduce the problem to a sequence of ordinary stopping problems, thus extending the results for deterministic times. This requires an extension of the underlying filtrations in general. Furthermore, we consider the Markovian case and treat an example explicitly. © 2013 Copyright Taylor and Francis Group, LLC.
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27.
  • Christensen, Sören, 1982, et al. (författare)
  • Optimal stopping of strong Markov processes
  • 2013
  • Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 123:3, s. 1138-1159
  • Tidskriftsartikel (refereegranskat)abstract
    • We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for Lévy processes obtained essentially via the Wiener-Hopf factorization. The main ingredient in our approach is the representation of the β-excessive functions as expected suprema. A variety of examples is given. © 2012 Elsevier B.V. All rights reserved.
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28.
  • Christensen, Sören, 1982 (författare)
  • Phase-type distributions and optimal stopping for autoregressive processes
  • 2012
  • Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 49:1, s. 22-39
  • Tidskriftsartikel (refereegranskat)abstract
    • Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications, the overshoot and the threshold time are of special interest. When the upward innovations are in the class of phase-type distributions, we determine the joint distribution of these two quantities and apply this result to problems of optimal stopping. Using a principle of continuous fit, this leads to explicit solutions. © 2012 Applied Probability Trust.
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29.
  • Christensen, Sören, 1982, et al. (författare)
  • Resolvent-Techniques for Multiple Exercise Problems
  • 2015
  • Ingår i: Applied Mathematics and Optimization. - : Springer Science and Business Media LLC. - 1432-0606 .- 0095-4616. ; 71:1, s. 95-123
  • Tidskriftsartikel (refereegranskat)abstract
    • © 2014, Springer Science+Business Media New York. We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristics of the problems can be identified more explicitly. We illustrate the main results with explicit examples.
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