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 different...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.展开更多
In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion （GSDEs） with integral-Lipschitz coefficients.
By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by G-Brownian motion.
基金supported by PRFU project N(Grant No.C00L03UN070120220004).
文摘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.
基金supported by the Major Program in Key Research Institute of Humanities and Social Sciences sponsored by Ministry of Education of China(under grant No.2009JJD790049)the Post-graduate Study Abroad Program sponsored by China Scholarship Council
文摘In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion （GSDEs） with integral-Lipschitz coefficients.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871153 and 11171262)
文摘By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by G-Brownian motion.
