A Study Of Reinsurance And Investment Equilibrium Strategies Of Insurance Companies Based On Stochastic Volatility Model

There is a complex relationship between the investment return on an insurance company’s capital and the risk it assumes.In order to balance this relationship,insurance companies need to transfer the risk by reinsuring the premiums to reduce the risk they take,and invest the retained premiums to gain income and increase their capital.The more premiums are ceded,the less premiums are retained and the less capital is available for investment,in which there is a premium balance problem.In contrast,there is an equilibrium relationship between reinsurance and investment under the objective of utility maximization.Therefore,by determining the equilibrium strategy between reinsurance and investment,insurance companies can balance the relationship between risk and return,maximize their capital appreciation,and improve their profitability and market competitiveness.However,the risks faced by insurance companies come from several aspects,including market risk,time lag risk,interest rate risk,etc.The changes of these risks have important effects on the reinsurance and investment strategies of insurance companies.For this reason,in this thesis,based on stochastic volatility model,considering the effect of time lag effect in nonfinancial market risk and interest rate stochasticity in financial market risk in the reinsurance and investment problems of insurance companies,we choose diffusion approximation model as the risk model of insurance companies,calculate reinsurance premiums based on variance premium principle,and use methods such as stochastic optimal control theory,dynamic programming principle,and stochastic analysis principle.We conduct an in-depth study from the following aspects.(1)We consider the influence of time lag effect on the equilibrium decision of insurance companies,assume that the price of risky assets obeys the Heston model,we take the exponential utility function of maximizing the absolute and relative wealth of insurance companies at the terminal moment as the objective,and study the reinsurance and investment equilibrium strategies of insurance companies;with the help of dynamic programming method,variable separation method and variable replacement method,we obtain the equilibrium strategies.(2)We further consider the impact of the risk brought by the stochastic fluctuations of interest rates in the financial market on the reinsurance and investment equilibrium strategies of insurance companies.Among them,the interest rate is described by the Cox-Ingersoll-Ross(CIR)model,and the price of risky assets obeys the Heston stochastic volatility model.To make the financial market richer and the model more realistic,zero-coupon bonds are added to the investment assets.The Hamilton-Jacobi-Bellman(HJB)equation of the objective function is established using stochastic optimal control theory,and the expression of the equilibrium strategy of the insurance company under the variance premium principle is derived using the Legendre pairwise transformation method.(3)We conduct numerical experiments and analyze the results of reinsurance and investment problems of insurance companies,and perform sensitivity analysis on the relevant parameters to obtain the dynamic changes of the relationship between the relevant parameters and the equilibrium strategy,and match them with the real situation.From the results of model building and parameter sensitivity analysis,the equilibrium strategy solutions of reinsurance and investment for insurance companies derived in this thesis are more in line with the facts.We summarize the results to know that(1)the changes of time lag information parameters affect the size of the weight of historical returns of insurance companies,the longer the memory time of the wealth process,the greater the weight of historical returns,and the insurance company operators will choose more aggressive investment strategies;(2)considering the risky asset price model and the stochastic factor model will change the decision choice of operators,such as insurance companies with higher risk aversion factors tend to choose a more conservative strategy,and factors such as the average speed of interest rate regression and volatility will affect insurers’ investments in risky assets,risk-free assets,and zero-coupon bonds.In conclusion,this thesis constructs a more realistic and economically meaningful reinsurance and investment model for insurance companies by considering both non-financial market risk and financial market risk.The research results obtained in this thesis are not only informative for insurance company operators to choose reinsurance and investment equilibrium strategies,but also provide a theoretical basis for the subsequent research on stochastic control problems in the financial field.