Article2017

Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information

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Stochastic processes and financial applications Stability and Control of Uncertain Systems Nonlinear Differential Equations Analysis

Abstract

Abstract This paper deals with the risk‐sensitive control problem for mean‐field stochastic delay differential equations (MF‐SDDEs) with partial information. Firstly, under the assumptions that the control domain is not convex and the value function is non‐smooth, we establish a stochastic maximum principle (SMP). Then, by means of Itô's formula and some continuous dependence, we prove the existence and uniqueness results for another type of MF‐SDDEs. Meanwhile, the verification theorem for the MF‐SDDEs is obtained by using a clever construction of the Hamiltonian function. Finally, based on our verification theorem, a linear‐quadratic system is investigated and the optimal control is also derived by the stochastic filtering technique.

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2007Mean field games 2013Probabilistic Analysis of Mean-Field Games 2010A Maximum Principle for SDEs of Mean-Field Type 2011A General Stochastic Maximum Principle for SDEs of Mean-field Type 2010Maximum principle for the stochastic optimal control problem with delay and application 2012ANTICIPATED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS 1 2009Anticipated backward stochastic differential equations 2003BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations

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2020Discrete‐time mean‐field stochastic linear‐quadratic optimal control problem with finite horizon 2017Infinite horizon optimal control problem of mean-field backward stochastic delay differential equation under partial information

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