In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rat...In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.展开更多
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 ...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.展开更多
基金supported by the Fundamental Research Funds for the SUFE No.2020110294supported by the National Natural Science Foundation of China,Grant No.71871202.
文摘In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.
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).
文摘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.
