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تسجيل مستخدم جديدPath-Dependent Optimal Stochastic Control and Viscosity Solution of Associated Bellman Equations
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In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent fully nonlinear partial differential equation of second order. A novel notion of viscosity solutions is introduced. Using Dupires functional It^o calculus, we characterize the value functional of the optimal stochastic control problem as the unique viscosity solution to the associated path-dependent Bellman equation.
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