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ANALYSE STOCHASTIQUE --- EQUATIONS DIFFERENTIELLES --- EQUATIONS DIFFERENTIELLES STOCHASTIQUES --- RESOLUTION NUMERIQUE

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This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.

Business mathematics. --- Diffusion processes. --- Mathematics, Applied. --- Diffusion processes --- Business mathematics --- Business & Economics --- Economic Theory --- Financial instruments. --- Finance. --- Funding --- Funds --- Capital instruments --- Financial instruments --- Law and legislation --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Macroeconomics. --- Quantitative Finance. --- Macroeconomics/Monetary Economics//Financial Economics. --- Applications of Mathematics. --- Economics --- Currency question --- Legal instruments --- Negotiable instruments --- Math --- Science --- Economics, Mathematical . --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematical economics --- Econometrics --- Mathematics --- Methodology

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This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.

Quantitative methods (economics) --- Finance --- Economics --- Mathematics --- Financial analysis --- financieel management --- toegepaste wiskunde --- economie --- financiële analyse --- wiskunde --- Mathématiques --- Finances --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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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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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.

Statistical science --- Finance --- Economics --- Operational research. Game theory --- Mathematical statistics --- Probability theory --- Mathematics --- Applied physical engineering --- Business economics --- kennis --- toegepaste wiskunde --- waarschijnlijkheidstheorie --- stochastische analyse --- economie --- statistiek --- financiën --- econometrie --- wiskunde --- kansrekening