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Jump processes.

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During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Levy processes are beyond their reach. Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations.Topics covered in this book include: jump-diffusion models, Levy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms. This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.

Stochastic processes --- Finance --- Jump processes. --- Finances --- Processus de sauts --- Mathematical models. --- Modèles mathématiques --- Jump processes --- Mathematical models --- mathematische modellen, toegepast op economie --- stochastische modellen --- opties --- risk management --- -Jump processes --- 332.01519233 --- Processes, Jump --- Markov processes --- Funding --- Funds --- Economics --- Currency question --- Modèles mathématiques --- Finance - Mathematical models

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In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Electronic books. -- local. --- Jump processes. --- Stochastic differential equations. --- Stochastic differential equations --- Jump processes --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Processes, Jump --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Quantitative Finance. --- Markov processes --- Differential equations --- Fokker-Planck equation --- Distribution (Probability theory. --- Finance. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Funding --- Funds --- Economics --- Currency question --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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This book focuses on the stability analysis of Markovian jump systems (MJSs) with various settings and discusses its applications in several different areas. It also presents general definitions of the necessary concepts and an overview of the recent developments in MJSs. Further, it addresses the general robust problem of Markovian jump linear systems (MJLSs), the asynchronous stability of a class of nonlinear systems, the robust adaptive control scheme for a class of nonlinear uncertain MJSs, the practical stability of MJSs and its applications as a modelling tool for networked control systems, Markovian-based control for wheeled mobile manipulators and the jump-linear-quadratic (JLQ) problem of a class of continuous-time MJLSs. It is a valuable resource for researchers and graduate students in the field of control theory and engineering.

Engineering. --- System theory. --- Mathematical models. --- Control engineering. --- Control. --- Systems Theory, Control. --- Mathematical Modeling and Industrial Mathematics. --- Jump processes. --- Processes, Jump --- Markov processes --- Systems theory. --- Control and Systems Theory. --- Models, Mathematical --- Simulation methods --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy

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This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: study of the stability problem for SMJSs with general transition rate matrices (TRMs); stabilization for SMJSs  by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; mode-dependent and mode-independent H∞ control solutions with development of a type of disordered controller; observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; consideration of robust H∞ filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays. Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course.  .

Engineering. --- Control. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Systems theory. --- Distribution (Probability theory). --- Ingénierie --- Distribution (Théorie des probabilités) --- Distribution (Probability theory. --- Jump processes. --- Queuing theory. --- Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Processes, Jump --- System theory. --- Probabilities. --- Control engineering. --- Markov processes --- Control and Systems Theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy