| 1. |
- Lundengård, Karl, 1987-
(författare)
-
Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions
- 2019
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis discusses two topics, finding the extreme points of the Vandermonde determinant on various surfaces and phenomenological modelling using power-exponential functions. The relation between these two problems is that they are both related to methods for curve-fitting. Two applications of the mathematical models and methods are also discussed, modelling of electrostatic discharge currents for use in electromagnetic compatibility and modelling of mortality rates for humans. Both the construction and evaluation of models is discussed.In the first chapter the basic theory for later chapters is introduced. First the Vandermonde matrix, a matrix whose rows (or columns) consists of monomials of sequential powers, its history and some of its properties are discussed. Next, some considerations and typical methods for a common class of curve fitting problems are presented, as well as how to analyse and evaluate the resulting fit. In preparation for the later parts of the thesis the topics of electromagnetic compatibility and mortality rate modelling are briefly introduced.The second chapter discusses some techniques for finding the extreme points for the determinant of the Vandermonde matrix on various surfaces including spheres, ellipsoids and cylinders. The discussion focuses on low dimensions, but some results are given for arbitrary (finite) dimensions.In the third chapter a particular model called the p-peaked Analytically Extended Function (AEF) is introduced and fitted to data taken either from a standard for electromagnetic compatibility or experimental measurements. The discussion here is entirely focused on currents originating from lightning or electrostatic discharges.The fourth chapter consists of a comparison of several different methods for modelling mortality rates, including a model constructed in a similar way to the AEF found in the third chapter. The models are compared with respect to how well they can be fitted to estimated mortality rate for several countries and several years and the results when using the fitted models for mortality rate forecasting is also compared.
|
|
| 2. |
- Murara, Jean-Paul, 1978-
(författare)
-
Market Models with Stochastic Volatility
- 2019
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Financial Markets is an interesting wide range area of research in Financial Engineering. In this thesis, which consists of an introduction, six papers and appendices, we deal with market models with stochastic volatility in order to understand some financial derivatives, mainly European options. Stochastic volatility models appear as a response to the weakness of the constant volatility models. Paper A is presented as a survey of different models where the volatility is itself a stochastic process and we present the techniques of pricing European options. Comparing single factor stochastic volatility models to constant factor volatility models, it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large fluctuations in the volatility levels and slope. We propose also a new model which is a variation of the Chiarella and Ziveyi model and we use the first order asymptotic expansion methods to determine the price of European options. Multiscale stochastic volatility models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. In paper B , we present an asymptotic expansion for the option price. We provide experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices are compared to the approximation obtained by Chiarella and Ziveyi. In paper C , we implement and analyze the Regime-Switching GARCH model using real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justified by the so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price difference criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coefficient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model. In paper D , we consider a market model with four correlated factors and two stochastic volatilities which is the same model as the one introduced in paper A and used in paper B . An advanced Monte Carlo method is used to find the no-arbitrage price of the European call option in the considered model. In paper E , we forecast the stochastic volatility for exchange rates using Exponential Weighted Moving Average (EWMA) model and study the effect of the out-of-sample periods and also the effect of the decay factor on the forecasts. In Paper F , considering a two-dimensional Black-Scholes equation, we compare the performances between the Crank-Nicolson scheme and the lognormality condition when pricing the European options. We do this by studying the effects of different parameters.
|
|
| 3. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 1
- 2019
-
Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1387-5841 .- 1573-7713. ; 21:3, s. 945-964
-
Tidskriftsartikel (refereegranskat)abstract
- New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders.
|
|
| 4. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2
- 2019
-
Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1387-5841 .- 1573-7713. ; 21:3, s. 965-984
-
Tidskriftsartikel (refereegranskat)abstract
- Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of sequen- tial phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces.
|
|
| 5. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Coupling and Ergodic Theorems for Markov Chains with Damping Component
- 2019
-
Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 101, s. 212-231
-
Tidskriftsartikel (refereegranskat)abstract
- Coupling method is used for geting ergodic theorems for perturbed Markov chains with damping component and rates of convergence in such theorems.
|
|
| 6. |
- Weishaupt, Hrafn Holger
(författare)
-
Graph theory based approaches for gene prioritization in biological networks : Application to cancer gene detection in medulloblastoma
- 2019
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Networks provide an intuitive and highly adaptable means to model relationships between objects. When translated to mathematical graphs, they become further amenable to a plethora of mathematical operations that allow a detailed study of the underlying relational data. Thus, it is not surprising that networks have evolved to a predominant method for analyzing such data in a vast variety of research fields. However, with increasing complexity of the studied problems, application of network modeling also becomes more challenging. Specifically, given a process to be studied, (i) which interactions are important and how can they be modeled, (ii) how can relationships be inferred from complex and potentially noisy data, and (iii) which methods should be used to test hypotheses or answer the relevant questions? This thesis explores the concept and challenges of network analysis in the context of a well-defined application area, i.e. the prediction of cancer genes from biological networks, with an application to medulloblastoma research.Medulloblastoma represents the most common malignant brain tumor in children. Currently about 70% of treated patients survive, but they often suffer from permanent cognitive sequelae. Medulloblastoma has previously been shown to harbor at least four distinct molecular subgroups. Related studies have also greatly advanced our understanding of the genetic aberrations associated with MB subgroups. However, to translate such findings to novel and improved therapy options, further insights are required into how the dysregulated genes interact with the rest of the cellular system, how such a cross-talk can drive tumor development, and how the arising tumorigenic processes can be targeted by drugs. Establishing such understanding requires investigations that can address biological processes at a more system-wide level, a task that can be approached through the study of cellular systems as mathematical networks of molecular interactions.This thesis discusses the identification of cancer genes from a network perspective, where specific focus is placed on one particular type of network, i.e. so called gene regulatory networks that model relationships between genes at the expression level. The thesis outlines the bridge between biological and mathematical network concepts. Specifically, the computational challenge of inferring such networks from molecular data is presented. Mathematical approaches for analyzing these networks are outlined and it is explored how such methods might be affected by network inference. Further focus is placed on dealing with the challenges of establishing a suitable gene expression dataset for network inference in MB. Finally, the thesis is concluded with an application of various network approaches in a hypothesis-driven study in MB, in which various novel candidate genes were prioritized.
|
|
| 7. |
- Abola, Benard, et al.
(författare)
-
A Variant of Updating Page Rank in Evolving Tree graphs
- 2019
-
Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 31-49
-
Konferensbidrag (refereegranskat)abstract
- PageRank update refers to the process of computing new PageRank values after change(s) (addition or removal of links/vertices) has occurred in real life networks. The purpose of the updating is to avoid recalculating the values from scratch. To efficiently carry out the update, we consider PageRank as the expected number of visits to target vertex if multiple random walks are performed, starting at each vertex once and weighing each of these walks by a weight value. Hence, it might be looked at as updating non-normalised PageRank. In the proposed approach, a scaled adjacency matrix is sequentially updated after every change and the levels of the vertices being updated as well. This enables sets of internal and sink vertices dependent on their roots or parents, thus vector-vector product can be performed sequentially since there are no infinite steps from one vertex to the other.
|
|
| 8. |
- Albuhayri, Mohammed, et al.
(författare)
-
Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model
- 2019
-
Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 81-90
-
Konferensbidrag (refereegranskat)abstract
- The double-mean-reverting model by Gatheral [1] is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the- money. Using the method by Pagliarani and Pascucci [6], we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.
|
|
| 9. |
- Anguzu, Collins, et al.
(författare)
-
A comparison of graph centrality measures based on random walks and their computation
- 2019
-
Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 121-135
-
Konferensbidrag (refereegranskat)abstract
- When working with a network it is often of interest to locate the "most important" nodes in the network. A common way to do this is using some graph centrality measures. Since what constitutes an important node is different between different networks or even applications on the same network there is a large amount of different centrality measures proposed in the literature. Due to the large amount of different centrality measures proposed in different fields, there is also a large amount very similar or equivalent centrality measures in the sense that they give the same ranks. In this paper we will focus on centrality measures based on powers of the adjacency matrix or similar matrices and those based on random walk in order to show how some of these are related and can be calculated efficiently using the same or slightly altered algorithms.
|
|
| 10. |
- Armakan, Abdoreza, et al.
(författare)
-
Enveloping algebras of color hom-Lie algebras
- 2019
-
Ingår i: Turkish Journal of Mathematics. - : SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK. - 1300-0098 .- 1303-6149. ; 43:1, s. 316-339
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincare- Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
|
|
