Work

A Hilbert space method to LQ optimal control of conditional McKean–Vlasov dynamics

Year: 2026

Type: article

Abstract: In this paper, we employ a Hilbert space approach based on orthogonal decomposition to investigate an optimal control problem associated with a linear conditional McKean–Vlasov dynamic, where the control process is allowed to be adapted to the filtration generated by both common and idiosyncratic noises under random coefficients. By applying the stochastic maximum principle, we derive the optimal feedback control and characterize the corresponding value function in terms of backward stochastic Riccati differential equations. Furthermore, an application to conditional mean–variance portfolio selection in an incomplete market setting is provided.

Source: Systems & Control Letters

DOI: 10.1016/j.sysconle.2026.106356

Authors: Liangquan Zhang, Xun Li

Institutions: Renmin University of China, Hong Kong Polytechnic University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,910

Funders: National Natural Science Foundation of China, Renmin University of China, Fundamental Research Funds for the Central Universities