Malliavin Calculus Applied to Optimal Control of Stochastic Partial Differential Equations with Jumps
نویسندگان
چکیده
In this paper we employ Malliavin calculus to derive a general stochastic maximum principle for stochastic partial differential equations with jumps under partial information. We apply this result to solve an optimal harvesting problem in the presence of partial information. Another application pertains to portfolio optimization under partial observation.
منابع مشابه
Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps
Abstract. We present various versions of the maximum principle for optimal control of forwardbackward stochastic differential equations (SDE) with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by Lévy...
متن کاملMaximum Principles of Markov Regime-Switching Forward-Backward Stochastic Differential Equations with Jumps and Partial Information
Résumé/Abstract: In this talk, we present three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jump-diffusion model is developed. After, an equi...
متن کاملTitle Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions
We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H > 1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential eq...
متن کاملIntegration by parts formula and applications to equations with jumps
We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bismut and Bichteler, Gravereaux and Jacod fails. 2000 MSC. Primary: 60H07, Secondary 60G51
متن کاملOptimal Control with Partial Information for Stochastic Volterra Equations
In the first part of the paper, we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus approach, we deduce a general maximum principle for optimal control of general stochastic Volterra equations. AMS Subject Classification: Primary 60H15 Secondary 93E20, 35R60.
متن کامل