Research On Optimal Investment-Reinsurance Strategy Based On Robust Control Theory

As the development of the financial market,the risk from the financial market is becoming more and more complex.As an important part of the financial market,insurance companies have an important impact on the financial market by taking on the risk business and the promotion of investment funds.In the face of the same industry incentive competition,insurance companies will generally improve their competitiveness from two aspects:on the first hand,they disperse risks by purchasing reinsurance business;on the other hand,idle funds are invested in financial markets to increase returns.At present,the diversified development pattern of insurance companies further increases the possibility that insurance companies are being eliminated.Because the insurance company's operation involves many aspects of interest,its elimination will affect the stability of the entire financial system.Therefore,how to get the optimal investment and reinsurance strategy of insurance company,especially with model uncertainty investment-reinsurance problem has become the focus of this paper.Firstly,we introduce the research background and main research status of insurance company investment in the first chapter.The second chapter introduces some basic preparatory knowledge used in this paper.In the third chapter,the optimal investment reinsurance problem with model uncertainty under stochastic volatility model is studied.In order to improve the strength for the competition,insurance companies allow the purchase of proportional reinsurance to diversify the risk and invest in the financial market for asset allocation.Besides,the financial market consists of a risk-free asset(bond)and a risk asset(stock).The volatility of risky assets follows the Heston stochastic volatility model and depicts the claims process of an insurance company by a Brown motion with drift.In order to help the ambiguity-averse decision maker obtain a robust optimal investment reinsurance strategy,the portfolio model under the ambiguity-neutral environment is transformed into the ambiguity-aversion environment,namely the model uncertainty environment,according to the Girsanov's theorem.By using the robust control principle,a maximum objective function with ambiguity-aversion coefficient is established and the corresponding HJB equation is obtained.We finally solve the optimal investment reinsurance policy under the model uncertainty environment.The fourth chapter assumes that the interest rate of the financial market invested by the insurance company is stochastic.The interest rate process is characterized by the Vasicek stochastic interest rate model,and the volatility satisfies the Heston stochastic volatility model.Under the double stochastic financial market environment,the explicit solution of optimal investment reinsurance policy of insurance company under fuzzy aversion environment is obtained by using the similar method.Finally,a numerical example is given to illustrate how the insurance company's investment reinsurance strategy will change when the interest rate and volatility of the financial market are both stochastic.The fifth chapter gives the conclusions and prospects of the article,the shortcomings and the direction of further research.