Work

Time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations

Year: 2024

Type: article

Abstract: We study the time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research makes two contributions. Firstly, we introduce a novel type of Riccati equation system with parameters and constraint conditions, known as the generalized equilibrium Riccati equation. This equation system offers a comprehensive solution for the closedloop equilibrium strategy of the problem at hand. Secondly, we establish the well-posedness of the generalized equilibrium Riccati equation for the one-dimensional case, provided certain conditions are met.

Source: Springer Link (Chiba Institute of Technology)

DOI: 10.1051/cocv/2024064/pdf

Authors: Qi Lü, Bowen Ma

Institutions: Sichuan University, Chengdu University of Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Sichuan University

Awards: G358573626, G6963497035, G7538126418