Controlled Markov Processes and Viscosity Solutions: v.25 - Rilegato

Fleming, Wendell H.; Soner, H. Mete

Rilegato

ISBN 10: 0387979271 ISBN 13: 9780387979274

Casa editrice: Springer Verlag, 1992

Riassunto

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. 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.

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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. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes, this becomes a nonlinear partial differential equation of second order, called a Hamilton-Jacobi-Bellman (HJB) equation. Typically, the value function is not smooth enough to satisfy the HJB equation in a classical sense. Viscosity solutions provide framework in which to study HJB equations, and to prove continuous dependence of solutions on problem data. The theory is illustrated by applications from engineering, management science, and financial economics.

Dettagli dell?edizione

• Editore: Springer Verlag
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 0387979271
• ISBN 13: 9780387979274
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 452
• Contatto del produttore: non disponibile