Wu, Tao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 56-61). / Abstracts in English and Chinese. / Chapter 1 --- Background and Organization --- p.7 / Chapter 2 --- Parallel Talbot method for solving partial integro- differential equations --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Initial-boundary value problem --- p.11 / Chapter 2.3 --- Spatial discretization and semidiscrete problem --- p.12 / Chapter 2.4 --- Parallel Talbot method --- p.15 / Chapter 2.4.1 --- Φ-functions and Talbot quadrature --- p.15 / Chapter 2.4.2 --- Control on nonnormality and feasibility con- straints --- p.18 / Chapter 2.4.3 --- Optimal parameterization of parabolic Talbot contour --- p.22 / Chapter 2.5 --- Numerical experiments --- p.26 / Chapter 2.6 --- Conclusion --- p.32 / Chapter 3 --- Memory-reduction Monte Carlo method for pricing American options --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Exponential Levy processes and the full-storage method --- p.39 / Chapter 3.3 --- Random number generators --- p.41 / Chapter 3.4 --- The memory-reduction method --- p.43 / Chapter 3.5 --- Numerical examples --- p.45 / Chapter 3.5.1 --- Black-Scholes model --- p.46 / Chapter 3.5.2 --- Merton's jump-diffusion model --- p.48 / Chapter 3.5.3 --- Variance gamma model --- p.50 / Chapter 3.5.4 --- Remarks on the efficiency of the memory-reduction method --- p.52 / Chapter 3.6 --- Conclusion --- p.53 / Chapter 3.7 --- Appendix --- p.54

We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field.

This dissertation includes two topics. For the first topic about the housing price jump risk, we use EM gradient algorithms to estimate parameters of the jump diffusion model and test whether the US monthly housing price have jump risk during 1986 to 2006. Then, in order to obtain a viable pricing framework of mortgage insurance contracts, this paper uses the jump diffusion processes of Merton (1976) to model the dynamic process of housing price. Using this model, we investigate the impact of price jump risk on the valuation of mortgage insurance premium from jump intensity, abnormal volatility of jump size and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on the mortgage insurance premium. For the second topic about the catastrophe risk, we investigate that, for catastrophic events, the assumption that catastrophe claims occur in terms of the Poisson process seems inadequate as it has constant intensity. We propose Markov Modulated Poisson process to model the arrival process for catastrophic events. Under this process, the underlying state is governed by a homogenous Markov chain, and it is the generalization of Cummins and Geman (1993, 1995), Chang, Chang, and Yu (1996), Geman and Yor (1997) and Vaugirard (2003a, 2003b). We apply Markov jump diffusion model to derive pricing formulas for catastrophe insurance products, included catastrophe futures call option, catastrophe PCS call spread and catastrophe bond. We use the data of PCS index and the annual number of hurricane events during 1950 to 2004 to test the quality of the fitting under the Markov Modulated Poisson process and the Poisson process. We reach the conclusion that the Markov Modulated Poisson process is fitter than the Poisson process and Weiner process in modeling the arrival rate of hurricane events when pricing three insurance products. Hence, if different status of climate environment has significant different arrival intensity in real economy, using jump diffusion model to evaluate CAT insurance products could cause significant mispricing.

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Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 108-118).

This thesis develops diffusion models for modern electrochemical experiments involving the transport of particles to electrodes and adsorbing surfaces. In particular, the models are related to the 'impact' method where particles stochastically arrive at an electrode and detected electrochemically. The studies are carried out using numerical simulations and also analytical methods. Chapter 1 is introductory and outlines some fundamental concepts in mass transport and kinetics, and their relation to electrochemical measurements which are of importance for the reader. Chapter 2 describes the numerical methods which are used for electrochemical simulations. Chapter 3 focuses on a specific two dimensional simulation system and the development of a high performance voltammetry simulation. Chapters 4 and 5 study the stochastic impacts of particles at an electrode surface. In Chapter 4, a 'diffusion only' model is developed using a probabilistic study and random walk simulations in order to provide expressions that can be used in so-called `impact' experiments. In Chapter 5, the practical cases of microdisc and microwire electrodes are investigated. Expressions for the number of impacts are developed and the concept of the lower limit of detection in ultra-dilute solutions is introduced. Then, a comparison study between the microwire electrode and the microdisc electrode explores a geometrical effect and its implications for experimental setups. In Chapter 6, a numerical and analytical study is developed to examine the effect of hindered diffusion as a particle moves close to an adsorbing surface. The study identifies the conditions under which this hindered diffusion is signiffcant even in a non-confined space. The study shows that the domination of hindered diffusion is strongly dependant on the sizes of both the particle and the target. The study focuses on a variety of target shapes and allows the number of hits/impacts to be estimated in practical 'impact' experiments. Moreover, a drastic effect on the calculation of the mean first passage time is observed for a sub-micron sized target, showing the importance of this effect not only for electrochemistry but also in biological systems. Chapters 7 and 8 investigate the properties of an adsorbing insulating surface adjacent to an electrode. In Chapter 7, a numerical study of the effect of 'shielding' by the insulating sheath is carried out. The study examines the in uence of this effect on the magnitude of the current in chronoamperometry experiments. Chapter 8 explores the case of reversible adsorption on the insulating surface for voltammetric enhancement by pre-concentration on the sheath surface. The results identify the conditions under which enhancement of the voltammetric signal can be observed. Finally, Chapter 9 looks at geometrical effects on the current response of insulating particles modified with an electroactive surface layer. Numerical models are developed to model the diffusion of charge transfer between electro-active sites on a modified surface of insulating particles. The current-time responses are simulated for particles with the shape of a sphere, a cube/cuboid, and a cylinder on an electrode. The characteristic currenttime responses are calculated for the various shapes. The observations show that the model can be utilised in experiments to determine the coverage or the diffusion coeficient of charge dissipation on modified insulating particles and, in some situations to identify the particle shape.

Cette thèse est consacrée au problème d'estimation de la fonction de dérive de certains modèles de processus stochastiques périodiques lorsque la durée d'observation tend vers l'infini. Aucune hypothèse de récurrence n'est posée a priori.Dans un premier temps nous considérons le modèle du type signal plus bruit dζt = f (t, θ)dt + σ(t)dWt,; et puis nous étudions l'estimation du paramètre θ à partir d'une observation continue et puis d'une observation discrète du processus {ζt} sur l'intervalle [0; T]. Les fonctions f (·, ·) et σ(·) sont continues et périodiques en t de même période P > 0, σ(·) > 0 et θ ∈ Θ ⊂R. Nous établissons la convergence en probabilité d'un estimateur du maximum de vraisemblance θˆT , sa normalité asymptotique et son efficacité asymptotique minimax. Lorsque f (t, θ) = θf (t), l'expression de θˆT est explicite et nous obtenons la convergence en moyenne quadratique aussi bien pour le cas d'une observation continue que pour le cas d'une observation discrète. De plus, nous déduisons la convergence presque sûre dans le cas d'une observation continue.Dans la seconde partie nous traitons l'estimation non-paramétrique de la fonction f(_) pour les modèles périodiques du type signal plus bruit et du type Ornstein-Uhlenbeck donnés par dζt = f (t)dt + σ(t)dWt, dξt = f (t)ξtdt + dWt. Pour le premier modèle, un estimateur à noyau périodique est construit, la convergence en moyenne quadratique uniformément sur [0; P] et presque sûre de cet estimateur est établie ainsi que sa normalité asymptotique. Dans le cas du modèle d'Ornstein-Uhlenbeck, la convergence du biais ainsi que la convergence en moyenne quadratique uniformément sur [0; P] sont prouvées, et leurs vitesses de convergence sont étudiées. / In this thesis, we consider a drift estimation problem of a certain class of stochastic periodic processes when the length of observation goes to infinity. Firstly, we deal with the linear periodic signal plus noise model dζt = f (t, θ)dt + σ(t)dWt, ;and we study the parametric estimation from a continuous and discrete observation of the process f_tg throughout the interval [0; T]. Using the maximum likelihood method we show the existence of an estimator θˆT which is consistent, asymptotically normal and asymptotically efficient in the sens minimax. When f(t; _) = _f(t), the expression of ^_T is explicit and we obtain the mean square convergence in the both continuous and discrete observation cases. In addition, we deduce the strong consistency in the case of continuous observation.Secondly, we consider the nonparametric estimation problem of the function f(_) for the next two periodic models of type signal plus noise and Ornstein-Uhlenbeckd_t = f(t)dt + _(t)dWt; d_t = f(t)_tdt + dWt:For the signal plus noise model, we build a kernel estimator, the convergence in mean square uniformly over [0; P] and almost sure convergence are established, as well as the asymptotic normality. For the Ornstein-Uhlenbeck model, we prove the convergence uniformly over [0; P] of the bias and the mean square convergence. Moreover, we study the speed of these convergences.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22823号 / 理博第4633号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 矢野 孝次, 教授 泉 正己, 教授 日野 正訓 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The objective of the thesis “Critical Analysis of the new retail and estimation of its future development” is to present a close overview about retail real estate issue in Czech Republic. First chapters are focused on theoretical issues of the retail. The practical part is focused on space-time analysis of market characteristics in the Czech Republic, which provides theoretical insights and diffusion process of expansion of shopping centers. The outcome of this paper is an estimation of the future development of the new retail from the optimistic, realistic, and pessimistic views of the market characteristics, and a definition of the competitive parameters of the retail development.

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