The Problem Of Optimal Reinsurance Investment Under Heston's Stochastic Volatility Model

The insurance company is an enterprise that operating and man aging risk.For the sake of avoiding excessive risks in the future operation,which may lead to huge losses or even bankruptcy of the insurance company.On the one hand,insurance company share its risks through reinsurance.On the other hand,insurance company will make reasonable and effective investments to increase the stability of the operation.In recent decades,with the continuous development of China's insurance industry,many domestic and foreign experts and scholars have studied the optimal reinsurance-investment strategy of the insurance companies.In this paper,in order to better conform to the investment situation of insurance companies in the actual financial market,we consider the optimal reinsurance-investment problem of an ambiguity-averse insurer under Heston's SV model.First,we study the optimal reinsurance-investment strategy for an ambiguous-aversion insurer based on Heston's SV model under variable interest rates.As for an ambiguous-aversion insurer,after considering proportional reinsurance,we assume that allocates its surplus between the risk-free asset and the risky asset,where the price process of the risk-free asset follows the differential equation derived by deterministic interest rate function and the price process of the risky asset follows the Heston's stochastic volatility model,respectively.And we get the explicit solution of optimal reinsurance-investment strategy in CARA utility by using Girsanov transformation and dynamic programming approach under the uncertainty of the model.Finally,the numerical simulation and corresponding economic explanation are given.Then,we investigate a robust optimal reinsurance and investment strategy in the defaultable financial markets for an ambiguity-averse insurer.And assuming that the ambiguous-aversion insurer is allowed to purchase proportional reinsurance and to invest on a risk-free asset and a risky asset and a defaultable bond at any time.Under the uncertainty of the model,we get the explicit solution of optimal reinsurance-investment strategy in CARA utility by using Girsanov transformation and dynamic programming approach in the pre-default case and post-default case,respectively.Finally,the numerical simulation and its economic analysis are given.Finally,the summarize and forecast of the study and development of the full text are narrated.And we give some directions for further research and improvement combining some of the shortcomings of this paper.