G-stochastic maximum principle for risk-sensitive control problem and its applications  

作　　者：Meriyam Dassa Adel Chala 

机构地区：[1]Laboratory of Applied Mathematics,University of Mohamed Khider,P.O.Box 145,Biskra 07000,Algeria

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第4期463-484,共22页概率、不确定性与定量风险（英文）

基　　金：supported by PRFU project N(Grant No.C00L03UN070120220004).

摘　　要：This study advances the G-stochastic maximum principle(G-SMP)from a risk-neutral framework to a risk-sensitive one.A salient feature of this advancement is its applicability to systems governed by stochastic differential equations under G-Brownian motion(G-SDEs),where the control variable may influence all terms.We aim to generalize our findings from a risk-neutral context to a risk-sensitive performance cost.Initially,we introduced an auxiliary process to address risk-sensitive performance costs within the G-expectation framework.Subsequently,we established and validated the correlation between the G-expected exponential utility and the G-quadratic backward stochastic differential equation.Furthermore,we simplified the G-adjoint process from a dual-component structure to a singular component.Moreover,we explained the necessary optimality conditions for this model by considering a convex set of admissible controls.To describe the main findings,we present two examples:the first addresses the linear-quadratic problem and the second examines a Merton-type problem characterized by power utility.

关 键 词：Stochastic optimal control G-EXPECTATION G-Brownian motion G-Stochastic differential equation G-stochastic maximum principle Risk-sensitive control Logarithmic transformation 

分 类 号：O21[理学—概率论与数理统计]