Controlled Markov Processes and Viscosity Solutions

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November 2005



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.


Deterministic Optimal Control.
Viscosity Solutions.
Optimal Control of Markov Processes: Classical Solutions.
Controlled Markov Diffusions in ?n.
Viscosity Solutions: Second-Order Case.
Logarithmic Transformations and Risk Sensitivity.
Singular Perturbations.
Singular Stochastic Control.
Finite Difference Numerical Approximations.
Applications to Finance.
Differential Games.
EAN: 9780387260457
ISBN: 0387260455
Untertitel: 'Stochastic Modelling and Applied Probability'. 2nd ed. 2006. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: November 2005
Seitenanzahl: 448 Seiten
Format: gebunden
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