Stochastic Modelling and Applied Probability

By: Halil Mete Soner, Wendell H. Fleming

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Hardcover | 17 November 2005 | Edition Number 2

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Hardcover
448 Pages

Edition Type
Revised

Dimensions(cm)
16.6 x 30.4 x 3.3

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This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through illustrative examples and selective material, to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance. In this Second Edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.

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Published: 19th November 2010

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Deterministic optimal control	p. 1
Viscosity solutions	p. 57
Optimal control of Markov processes : classical solutions	p. 119
Controlled Markov diffusions in IR[superscript n]	p. 151
Viscosity solutions : second-order case	p. 199
Logarithmic transformations and risk sensitivity	p. 227
Singular perturbations	p. 261
Singular stochastic control	p. 293
Finite difference numerical approximations	p. 321
Applications to finance	p. 347
Differential games	p. 375
Duality relationships	p. 397
Dynkin's formula for random evolutions with Markov chain parameters	p. 399
Extension of Lipschitz continuous functions; smoothing	p. 401
Stochastic differential equations : random coefficients	p. 403
Table of Contents provided by Blackwell. All Rights Reserved.

Stochastic Modelling and Applied Probability

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Hardcover

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