2013/04/15 by Jiongmin Yong, Yong, Jiongmin · 3 citations
Economics, Econometrics and Finance · Social Sciences · #49N10 #49N70 #93E20 #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1304.3964
openalex publication_date 2013/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop equilibrium solutions are presented for such kind of problems. Open-loop solutions are presented by means of variational method with decoupling of forward-backward stochastic differential equations, which lead to a Riccati equation system lack of symmetry. Closed-loop solutions are presented by means of multi-person differential games, the limit of which leads to a Riccati equation system with a symmetric structure.