On the existence of optimal controls for backward stochastic partial differential equations

2016/12/06 by Qingxin Meng, Yang Shen, Meng, Qingxin +3
Economics, Econometrics and Finance · Social Sciences · #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1612.01664

openalex publication_date 2016/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward stochastic evolution equations. Under some growth and monotonicity conditions on the coefficients and suitable assumptions on the Hamiltonian function, the existence of the optimal control boils down to proving the uniqueness and existence of a solution to the stochastic Hamiltonian system, i.e. a fully coupled forward-backward stochastic evolution equation. Using some a prior estimates, we prove the uniqueness and existence via the method of continuation. Two examples of linear-quadratic control are solved to demonstrate our results.

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