Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain

Details Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain

2012-02-07

arxiv.org/abs/1202.1412v2

Mathematics

Probability

33 pages

Scientific paper

In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations developed by Pardoux and Zhang [17]. The value function is shown to be the viscosity solution to the associated Hamilton-Jacobi-Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. The method of stochastic "backward semigroups" introduced by Peng [18] is adapted to our context.

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