Controlled Markov Processes and Viscosity Solutions

Par : Wendell H. Fleming, Halil Mete Soner
    • Nombre de pages432
    • PrésentationBroché
    • FormatGrand Format
    • Poids0.69 kg
    • Dimensions15,5 cm × 23,5 cm × 2,4 cm
    • ISBN978-1-4419-2078-2
    • EAN9781441920782
    • Date de parution19/11/2010
    • CollectionStochastic Modelling
    • ÉditeurSpringer

    Résumé

    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
    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.