Applied Stochastic Control of Jump Diffusions
Applied Stochastic Control of Jump Diffusions

Author: Bernt Øksendal

Publisher: Springer Science & Business Media

Published: 2007-04-26

Total Pages: 263

ISBN-13: 3540698264

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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Applied Stochastic Processes and Control for Jump-Diffusions
Applied Stochastic Processes and Control for Jump-Diffusions

Author: Floyd B. Hanson

Publisher: SIAM

Published: 2007-01-01

Total Pages: 472

ISBN-13: 9780898718638

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This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems.

Numerical Methods for Stochastic Control Problems in Continuous Time
Numerical Methods for Stochastic Control Problems in Continuous Time

Author: Harold Kushner

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 480

ISBN-13: 146130007X

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Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Point Processes and Jump Diffusions
Point Processes and Jump Diffusions

Author: Tomas Björk

Publisher: Cambridge University Press

Published: 2021-06-17

Total Pages: 323

ISBN-13: 1316518671

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Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.

Stochastic Flows and Jump-Diffusions
Stochastic Flows and Jump-Diffusions

Author: Hiroshi Kunita

Publisher: Springer

Published: 2019-03-26

Total Pages: 366

ISBN-13: 9811338019

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This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.

Applied Stochastic Differential Equations
Applied Stochastic Differential Equations

Author: Simo Särkkä

Publisher: Cambridge University Press

Published: 2019-05-02

Total Pages: 327

ISBN-13: 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Applied Stochastic Control of Jump Diffusions
Applied Stochastic Control of Jump Diffusions

Author: Bernt Øksendal

Publisher: Springer

Published: 2009-09-02

Total Pages: 262

ISBN-13: 9783540834861

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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott
Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott

Author: Samuel N Cohen

Publisher: World Scientific

Published: 2012-08-10

Total Pages: 605

ISBN-13: 9814483915

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This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.

Modeling, Stochastic Control, Optimization, and Applications
Modeling, Stochastic Control, Optimization, and Applications

Author: George Yin

Publisher: Springer

Published: 2019-07-16

Total Pages: 593

ISBN-13: 3030254984

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This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.