Functionals Of Multidimensional Diffusions With Applications To Finance

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Functionals Of Multidimensional Diffusions With Applications To Finance

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Author : Jan Baldeaux
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13

Functionals Of Multidimensional Diffusions With Applications To Finance written by Jan Baldeaux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.

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.​

Affine Diffusions And Related Processes Simulation Theory And Applications

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Author : Aurélien Alfonsi
language : en
Publisher: Springer
Release Date : 2015-04-30

Affine Diffusions And Related Processes Simulation Theory And Applications written by Aurélien Alfonsi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-30 with Mathematics categories.

This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments. The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.

Monte Carlo And Quasi Monte Carlo Methods

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Author : Art B. Owen
language : en
Publisher: Springer
Release Date : 2018-07-03

Monte Carlo And Quasi Monte Carlo Methods written by Art B. Owen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Computers categories.

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.

Geometry And Invariance In Stochastic Dynamics

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Author : Stefania Ugolini
language : en
Publisher: Springer Nature
Release Date : 2022-02-09

Geometry And Invariance In Stochastic Dynamics written by Stefania Ugolini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-09 with Mathematics categories.

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Mathematical Modelling And Numerical Methods In Finance

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Author : Alain Bensoussan
language : en
Publisher: Elsevier
Release Date : 2009-06-16

Mathematical Modelling And Numerical Methods In Finance written by Alain Bensoussan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-16 with Mathematics categories.

Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. - Coverage of all aspects of quantitative finance including models, computational methods and applications - Provides an overview of new ideas and results - Contributors are leaders of the field

Stochastic Calculus Of Variations In Mathematical Finance

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Author : Paul Malliavin
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-25

Stochastic Calculus Of Variations In Mathematical Finance written by Paul Malliavin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-25 with Business & Economics categories.

Highly esteemed author Topics covered are relevant and timely

Discrete Time Semi Markov Random Evolutions And Their Applications

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Author : Nikolaos Limnios
language : en
Publisher: Springer Nature
Release Date : 2023-07-24

Discrete Time Semi Markov Random Evolutions And Their Applications written by Nikolaos Limnios and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-24 with Mathematics categories.

This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

Stochastic Analysis Stochastic Systems And Applications To Finance

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Author : Allanus Hak-Man Tsoi
language : en
Publisher: World Scientific
Release Date : 2011

Stochastic Analysis Stochastic Systems And Applications To Finance written by Allanus Hak-Man Tsoi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Business & Economics categories.

Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin

Marginal And Functional Quantization Of Stochastic Processes

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Author : Harald Luschgy
language : en
Publisher: Springer Nature
Release Date : 2023-12-06

Marginal And Functional Quantization Of Stochastic Processes written by Harald Luschgy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-06 with Mathematics categories.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

Reviews In Modern Quantitative Finance

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Author : Andrey Itkin
language : en
Publisher: World Scientific
Release Date : 2024-03-12

Reviews In Modern Quantitative Finance written by Andrey Itkin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-12 with Business & Economics categories.

This volume contains six chapters which cover several modern topics of quantitative finance and reflect the most significant trends currently shaping this field. The chapters discuss in detail and make original contributions to stochastic/fractional volatility models and their asymptotic solutions (Chapter 1); equity trading, optimal portfolios and related problems (Chapters 2, 5, 6); machine learning and NLP (Chapters 2, 3); and economic scenario generation (Chapter 4), and are written by the leading experts in the field. This book is useful for both researchers and practitioners.