2017/03/06 by Xun Li, Li, Xun, Yuan‐Hua Ni +3
Environmental Science · Social Sciences · #Analysis of environmental and stochastic processes #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1703.01942
openalex publication_date 2017/03/06 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/28
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium strategy. The open-loop equilibrium control is defined for a given initial pair, while the linear feedback equilibrium strategy is defined for all the initial pairs. Maximum-principle-type necessary and sufficient conditions containing stationary and convexity are derived for the existence of these two time-consistent solutions, respectively. Furthermore, for the case where the system matrices are independent of the initial time, we show that the existence of the open-loop equilibrium control for a given initial pair is equivalent to the solvability of a set of nonsymmetric generalized difference Riccati equations and a set of linear difference equations. Moreover, the existence of linear feedback equilibrium strategy is equivalent to the solvability of another set of symmetric generalized difference Riccati equations.