The authors consider a robust optimal reinsurance and investment problem in a risk model with two dependent classes of insurance business for an Ambiguity-Averse insurer(AAI).The insurer aims to minimize the goal-reac...The authors consider a robust optimal reinsurance and investment problem in a risk model with two dependent classes of insurance business for an Ambiguity-Averse insurer(AAI).The insurer aims to minimize the goal-reaching probability that the value of the wealth process reaches a low barrier before a high goal.Using the stochastic control approach based on the Hamilton-JacobiBellman(HJB)equation,the authors derive the robust optimal reinsurance and investment strategies,as well as the corresponding value function.The authors conclude that the robust optimal investmentreinsurance strategy coincides with the one without model ambiguity,but the value function differs.As a consequence,ignoring model uncertainty leads to significant value function loss for the AAI.Besides,it is worth noting that if the insurer has only one business,the sum of the degenerated value function and the one of(Luo,et al.,2019)is equal to 1 both for ambiguity and ambiguity-neutral.Finally,numerical examples are given to illustrate our results.展开更多
基金supported by the Natural Science Foundation of Hunan Province under Grant No.2023JJ30381the Changsha Municipal Natural Science Foundation under Grant No.kq2208159+2 种基金the Humanities and Social Science Fund of Ministry of Education of China under Grant No.23YJC910008the Graduate Research and Innovation Project of Hunan Province under Grant No.CX20230241the Graduate Research and Innovation Project of Central South University under Grant No.1053320222639。
文摘The authors consider a robust optimal reinsurance and investment problem in a risk model with two dependent classes of insurance business for an Ambiguity-Averse insurer(AAI).The insurer aims to minimize the goal-reaching probability that the value of the wealth process reaches a low barrier before a high goal.Using the stochastic control approach based on the Hamilton-JacobiBellman(HJB)equation,the authors derive the robust optimal reinsurance and investment strategies,as well as the corresponding value function.The authors conclude that the robust optimal investmentreinsurance strategy coincides with the one without model ambiguity,but the value function differs.As a consequence,ignoring model uncertainty leads to significant value function loss for the AAI.Besides,it is worth noting that if the insurer has only one business,the sum of the degenerated value function and the one of(Luo,et al.,2019)is equal to 1 both for ambiguity and ambiguity-neutral.Finally,numerical examples are given to illustrate our results.
