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

Juan Li; Shanjian Tang

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arXiv · 1202.1412

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

Juan Li·Shanjian Tang

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Abstract

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 [20]. The value function is shown to be the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. For this, we also prove some new estimates for stochastic differential systems reflected in a domain.

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BibTeX RIS

Juan Li, Shanjian Tang. 2012-02-07. Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain. https://arxiv.org/abs/1202.1412

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