Well-posedness of Stochastic Riccati Equations and Closed-Loop Solvability for Stochastic Linear Quadratic Optimal Control Problems

2018/11/18 by Qi Lü, Lü, Qi
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #49N10 #49N35 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1811.07338

openalex publication_date 2018/11/18 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28

Abstract

We study the closed-loop solvability of a stochastic linear quadratic optimal control problem for systems governed by stochastic evolution equations. This solvability is established by means of solvability of the corresponding Riccati equation, which is implied by the uniform convexity of the quadratic cost functional. At last, conditions ensuring the uniform convexity of the cost functional are discussed.

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