| 1. |
- Abola, Benard
(författare)
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Perturbed Markov Chains with Damping Component and Information Networks
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis brings together three thematic topics, PageRank of evolving tree graphs, stopping criteria for ranks and perturbed Markov chains with damping component. The commonality in these topics is their focus on ranking problems in information networks. In the fields of science and engineering, information networks are interesting from both practical and theoretical perspectives. The fascinating property of networks is their applicability in analysing broad spectrum of problems and well established mathematical objects. One of the most common algorithms in networks' analysis is PageRank. It was developed for web pages’ ranking and now serves as a tool for identifying important vertices as well as studying characteristics of real-world systems in several areas of applications. Despite numerous successes of the algorithm in real life, the analysis of information networks is still challenging. Specifically, when the system experiences changes in vertices /edges or it is not strongly connected or when a damping stochastic matrix and a damping factor are added to an information matrix. For these reasons, extending existing or developing methods to understand such complex networks is necessary.Chapter 2 of this thesis focuses on information networks with no bidirectional interaction. They are commonly encountered in ecological systems, number theory and security systems. We consider certain specific changes in a network and describe how the corresponding information matrix can be updated as well as PageRank scores. Specifically, we consider the graph partitioned into levels of vertices and describe how PageRank is updated as the network evolves.In Chapter 3, we review different stopping criteria used in solving a linear system of equations and investigate each stopping criterion against some classical iterative methods. Also, we explore whether clustering algorithms may be used as stopping criteria.Chapter 4 focuses on perturbed Markov chains commonly used for the description of information networks. In such models, the transition matrix of an information Markov chain is usually regularised and approximated by a stochastic (Google type) matrix. Stationary distribution of the stochastic matrix is equivalent to PageRank, which is very important for ranking of vertices in information networks. Determining stationary probabilities and related characteristics of singularly perturbed Markov chains is complicated; leave alone the choice of regularisation parameter. We use the procedure of artificial regeneration for the perturbed Markov chain with the matrix of transition probabilities and coupling methods. We obtain ergodic theorems, in the form of asymptotic relations. We also derive explicit upper bounds for the rate of convergence in ergodic relations. Finally, we illustrate these results with numerical examples.
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| 2. |
- Betuel, Canhanga, et al.
(författare)
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Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach
- 2018
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Konferensbidrag (refereegranskat)abstract
- The development of financial markets imposes more complex models on the option pricing problems. On the previous papers by the authors, we consider a model under which the underlying asset is driven by two independent Heston-type stochastic volatility processes of multiscale (fast and slow) mean-reverting rates and we compute an approximate solution for the option pricing problem, using asymptotic expansion method. In the present paper, we aim to calibrate the model using the market prices of options on Euro Stoxx 50 index and an equity stock in the European market. Our approach is to use the market implied volatility surface for calibrating directly a set of new parameters required in our second-order asymptotic expansion pricing formula for European options. This secondorder asymptotic expansion formula provides a better approximation formula for European option prices than the first-order formula, as explained in an earlier work of the authors.
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| 3. |
- Boulougari, Andromachi, et al.
(författare)
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Application of a power-exponential function-based model to mortality rates forecasting
- 2019
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Ingår i: Communications in Statistics: Case Studies, Data Analysis and Applications. - : Informa UK Limited. - 2373-7484. - 9786185180270 - 9786185180294 ; 5:1, s. 3-10
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Tidskriftsartikel (refereegranskat)abstract
- There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the “accident hump” occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee–Carter method will be discussed.
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| 4. |
- Canhanga, Betuel, 1980-, et al.
(författare)
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Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities
- 2018
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 47:6, s. 1328-1349
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Tidskriftsartikel (refereegranskat)abstract
- The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.
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| 5. |
- Canhanga, Betuel, 1980-, et al.
(författare)
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Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic Volatility
- 2017
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Ingår i: INCPAA 2016 Proceedings. - : Author(s). - 9780735414648 ; , s. 020035-1-020035-10
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Konferensbidrag (refereegranskat)abstract
- After Black-Scholes proposed a model for pricing European Option in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption in the Black-Scholes model was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced non-constant volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multi-factor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented an approximate formula for pricing American option.The huge calculation involved in the Chiarella and Ziveyi approach motivated us to investigate another approach to compute European option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present chapter we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.
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| 6. |
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Engineering Mathematics I : Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering
- 2016
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Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. In particular, it features mathematical methods and models of applied analysis, probability theory, differential equations, tensor analysis and computational modelling used in applications to important problems concerning electromagnetics, antenna technologies, fluid dynamics, material and continuum physics and financial engineering. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications. It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.
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| 7. |
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Engineering Mathematics II : Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization
- 2016
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Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation.The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications.It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.
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| 8. |
- Jankoski, Radoslav, et al.
(författare)
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Comparison of TL, Point-Matching and Hybrid Circuit Method Analysis of a Horizontal Dipole Antenna Immersed in Lossy Soil
- 2016
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Ingår i: Engineering Mathematics I. - Heidelberg : Springer. - 9783319420820 - 9783319420813 ; , s. 51-63
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Bokkapitel (refereegranskat)abstract
- HF analysis of a horizontal dipole antenna buried in lossy ground has been performed in this paper. The soil is treated as a homogenous half-space of known electrical parameters. The authors compare the range of applicability of two forms of transmission line model , a hybrid circuit method, and a point-matching method in such analysis.
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| 9. |
- Javor, V., et al.
(författare)
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A Study on Frequency Spectrum of Electrostatic Discharge Currents and Lightning Currents
- 2019
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Ingår i: 2019 14th International Conference on Advanced Technologies, Systems and Services in Telecommunications, TELSIKS 2019 - Proceedings. - : Institute of Electrical and Electronics Engineers Inc.. - 9781728108780 ; , s. 198-201
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Konferensbidrag (refereegranskat)abstract
- Electrostatic discharges (ESD) consequences are not only damages, but also very fast transients in electric circuits and devices, as well as in large power systems. This paper presents frequency spectrum analysis of the IEC 61000-4-2 standard current approximated by multi-peaked analytically extended function (MP-AEF) and of typical lightning currents according to the IEC 62305 standard. This analysis is important for the choice of protective devices and frequency range of measurement equipment used in experiments. A comparison of the measured and theoretical results is also given.
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| 10. |
- Javor, Vesna, et al.
(författare)
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Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation
- 2018
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Ingår i: IEEE transactions on electromagnetic compatibility (Print). - : IEEE. - 0018-9375 .- 1558-187X. ; 60:5, s. 1415-1426
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Tidskriftsartikel (refereegranskat)abstract
- Lightning discharge currents waveshapes and their derivatives with multiple peaks are measured in artificially triggered lightning experiments and at instrumented tall towers. Such waveshapes are represented in this paper by the N-peaked analytically extended function (NP-AEF) and Marquardt least-squares method is applied for the estimation of its nonlinear parameters. Typical channel-base currents of the first negative, subsequent negative strokes, and positive strokes, based on comprehensive measurements by Berger et al. at Monte San Salvatore in Switzerland, are approximated by NP-AEFs and used in the computation of lightning electromagnetic fields. A new attenuation factor introducing nonlinear current attenuation along the channel is applied within the modified transmission line model (MTLSIN). A lightning return stroke is assumed to have a vertical discharge channel at the perfectly conducting ground. In order to validate this model, calculated lightning electromagnetic fields are compared with the typical, as measured by Lin et al. at various distances from the discharges. Lightning currents and their derivatives measured at the tall towers are also approximated by NP-AEFs. For the measured artificially triggered lightning currents, MTLSIN is applied for the calculation of their electromagnetic fields. These are compared with the measured fields of specific lightning strokes, so as to results of other models.
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