Geodesic
Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain
Li, Juan1 ; Tang, Shanjian2
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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1150-1177

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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
Keywords: 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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     title = {Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1150--1177},
     publisher = {EDP-Sciences},
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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

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