Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *

2016/04/22 by Huyên Pham, Pham, Huyên · 4 citations
Decision Sciences · Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1604.06609

openalex publication_date 2016/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in [32], we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit in particular optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in incomplete market model.

Citations

• Bellman equation and viscosity solutions for mean-field stochastic control problem
• Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Closed-Loop Solvability

Cited by

• Robust mean-field control under common noise uncertainty
• Near Optimality of Discrete-Time Approximations for Controlled McKean-Vlasov Diffusions and Interacting Particle Systems
• Ergodicity of conditional McKean-Vlasov jump diffusions
• The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons

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