2023/06/26 by Teng Song, Bin Liu, Song, Teng +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #49N10 #93C55 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2306.14496
openalex publication_date 2023/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses the discrete-time mean-field stochastic linear quadratic optimal control problems, whose weighting matrices in the cost functional are not assumed to be definite. The open-loop solvability is characterized by the existence of the solution to a mean-field forward-backward stochastic difference equations with a convexity condition and a stationary condition. The closed-loop solvability is presented by virtue of the existences of the regular solution to the generalized Riccati equations and the solution to the linear recursive equation, which is also shown by the uniform convexity of the cost functional. Moreover, based on a family of uniformly convex cost functionals, the finiteness of the problem is characterized. Also, it turns out that a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem. Finally, some examples are given to illustrate the theory developed.