G-stochastic maximum principle for risk-sensitive control problem and its applications
作者机构：Laboratory of Applied MathematicsUniversity of Mohamed KhiderP.O.Box 145Biskra 07000Algeria
出 版 物：《Probability, Uncertainty and Quantitative Risk》 (概率、不确定性与定量风险（英文）)
年 卷 期：2023年第8卷第4期
页 面：463-484页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：supported by PRFU project N(Grant No.C00L03UN070120220004)
主 题：Stochastic optimal control G-expectation G-Brownian motion G-Stochastic differential equation G-stochastic maximum principle Risk-sensitive control Logarithmic transformation
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 *** aim to generalize our findings from a risk-neutral context to a risk-sensitive performance ***,we introduced an auxiliary process to address risk-sensitive performance costs within the G-expectation ***,we established and validated the correlation between the G-expected exponential utility and the G-quadratic backward stochastic differential ***,we simplified the G-adjoint process from a dual-component structure to a singular ***,we explained the necessary optimality conditions for this model by considering a convex set of admissible *** 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.
维普期刊数据库