A Heston local-stochastic volatility model for optimal investment-reinsurance strategy with a defaultable bond in an ambiguous environment  

作　　者：Ge Wang Menglei Huang Qing Zhou Weixing Wu Weilin Xiao 

机构地区：[1]School of Science,Key Laboratory of Mathematics and Information Networks,Ministry of Education,Beijing University of Posts and Telecommunications,Beijing 100876,China [2]School of Finance,Capital University of Economics and Business,Beijing 100070,China [3]School of Management,Zhejiang University,Hangzhou 310058,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第4期499-522,共24页概率、不确定性与定量风险（英文）

基　　金：isupported by the National Natural Science Foundation of China(Grant Nos.11871010 and 11971040);the Fundamental Research Funds for the Central Universities(Grant No.2019XD-A11);The work of Weilin Xiao is supported by the Humanities and Social Sciences of Ministry of Education Planning Fund of China(Grant No.23YJA630102).

摘　　要：This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.

关 键 词：Smooth ambiguity utility Heston local-stochastic volatility model Perturbation method Investment and reinsurance Defaultable bond 

分 类 号：O17[理学—数学]