Equilibrium for a Time-Inconsistent Stochastic Linear–Quadratic Control System with Jumps and Its Application to the Mean-Variance Problem

Zhongyang Sun () and Xianping Guo ()
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Zhongyang Sun: Qufu Normal University
Xianping Guo: Sun Yat-sen University

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 2, No 2, 383-410

Abstract: Abstract This paper studies a kind of time-inconsistent linear–quadratic control problem in a more general framework with stochastic coefficients and random jumps. The time inconsistency comes from the dependence of the terminal cost on the current state as well as the presence of a quadratic term of the expected terminal state in the objective functional. Instead of finding a global optimal control, we look for a time-consistent locally optimal equilibrium solution within the class of open-loop controls. A general sufficient and necessary condition for equilibrium controls via a flow of forward–backward stochastic differential equations is derived. This paper further develops a new methodology to cope with the mathematical difficulties arising from the presence of stochastic coefficients and random jumps. As an application, we study a mean-variance portfolio selection problem in a jump-diffusion financial market; an explicit equilibrium investment strategy in a deterministic coefficients case is obtained and proved to be unique.

Keywords: Time-inconsistent linear–quadratic control; Stochastic coefficients and random jumps; Equilibrium control; Forward–backward stochastic differential equation; Mean-variance portfolio selection; 91G80; 93E20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-018-01471-x

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