Optimal Reinsurance-Investment Strategy With Friction And Ambiguity Aversion

As special financial institutions operating risk,insurance companies could spread risk by purchasing reinsurance and realize hedging as well as appreciation of insurance funds through investment.Therefore,the research on optimal reinsurance and investment problems for insurance companies is becoming a focus in the actuarial field of applied statistics,with high academic value and broad application value.This paper derives an optimal reinsurance-investment strategy for an ambiguity-averse insurance company,who faces execution costs when trading a risky asset with return predictability.The surplus process of the insurance company is assumed to follow a spectrally negative Lévy process and the insurance company is assumed to be ambiguityaverse,which reflects her worry about model uncertainty.The insurance company can purchase proportional reinsurance or acquire new business and invest in a financial market,which consists of a risk-free asset and a risky asset,to manage its risk.The dynamics of the risky asset’s price is correlated with the insurance surplus.This paper aims to maximize the mean-variance preference on a finite time horizon.By solving the Hamilton-Jacobi-Bellman equation,closed-forms of optimal reinsurance-investment strategies are obtained under two kinds of transaction costs: one is purely temporary transaction costs and the other is temporary and persistent transaction costs.Finally,the simulations of optimal strategies are conducted with historical data of CSI 300 Index daily closing price and other market data,while numerical examples are provided to illustrate the economic implications of the findings.