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Author: Bernt Øksendal
Publisher: Springer Science & Business Media
ISBN: 3540698264
Category : Mathematics
Languages : en
Pages : 263
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Book Description
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.
Author: Bernt Øksendal
Publisher: Springer Science & Business Media
ISBN: 3540698264
Category : Mathematics
Languages : en
Pages : 263
Get Book Here
Book Description
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.
Author: Bernt Øksendal
Publisher: Springer
ISBN: 9783540834861
Category : Mathematics
Languages : en
Pages : 262
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Book Description
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.
Author: Floyd B. Hanson
Publisher: SIAM
ISBN: 9780898718638
Category : Mathematics
Languages : en
Pages : 472
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Book Description
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.
Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 146130007X
Category : Mathematics
Languages : en
Pages : 480
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Book Description
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.
Author: Floyd B. Hanson
Publisher: SIAM
ISBN: 0898716330
Category : Mathematics
Languages : en
Pages : 461
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Book Description
A practical, entry-level text integrating the basic principles of applied mathematics and probability, and computational science.
Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327
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Book Description
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author: Ivan Ivanov
Publisher: IntechOpen
ISBN: 9789535108306
Category : Mathematics
Languages : en
Pages : 286
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Book Description
Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.
Author: Hiroshi Kunita
Publisher: Springer
ISBN: 9811338019
Category : Mathematics
Languages : en
Pages : 352
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Book Description
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.
Author: Floyd B. Hanson
Publisher:
ISBN:
Category :
Languages : en
Pages : 44
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Book Description
An applied compact introductory survey of Markov stochastic processes and control in continuous time is presented. The presentation is in tutorial stages, beginning with deterministic dynamical systems for contrast and continuing on to perturbing the deterministic model with diffusions using Wiener processes. Then jump perturbations are added using simple Poisson processes constructing the theory of simple jump-diffusions. Next, marked-jump-diffusions are treated using compound Poisson processes to include random marked jump-amplitudes in parallel with the equivalent Poisson random measure formulation. Otherwise, the approach is quite applied, using basic principles with no abstractions beyond Poisson random measure. This treatment is suitable for those in classical applied mathematics, physical sciences, quantitative finance and engineering, but have trouble getting started with the abstract measure-theoretic literature. The approach here builds upon the treatment of continuous functions in the regular calculus and associated ordinary differential equations by adding non-smooth and jump discontinuities to the model. Finally, the stochastic optimal control of marked-jump-diffusions is developed, emphasizing the underlying assumptions. The survey concludes with applications in biology and finance, some of which are canonical, dimension reducible problems and others are genuine nonlinear problems.
Author: Tomas Björk
Publisher: Cambridge University Press
ISBN: 1316518671
Category : Business & Economics
Languages : en
Pages : 323
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Book Description
Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.
