Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1150-1177.

The paper is concerned with optimal control of a stochastic differential system reflected in a domain. The cost functional is implicitly defined via a generalized backward stochastic differential equation developed by Pardoux and Zhang [Probab. Theory Relat. Fields 110 (1998) 535–558]. 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. The proof requires new estimates for the reflected stochastic differential system.

Reçu le :
DOI : 10.1051/cocv/2014062
Classification : 60H99, 60H30, 35J60, 93E05, 90C39
Mots clés : Hamilton–Jacobi–Bellman equation, nonlinear Neumann boundary, value function, backward stochastic differential equations, dynamic programming principle, viscosity solution
Li, Juan 1 ; Tang, Shanjian 2

1 School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264200, P.R. China
2 Institute of Mathematics and Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
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Li, Juan; Tang, Shanjian. Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1150-1177. doi : 10.1051/cocv/2014062. http://archive.numdam.org/articles/10.1051/cocv/2014062/

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