Research On Insurer's Optimal Investment Strategy Under Constant Elasticity Of Variance (CEV) Model

Modern insurance industry has an important feature that underwriting business and insur-ance funds investment are paid equal attention, the two are known as the development of the insurance industry's "two wheels", and have great significance to it. As the high marketing degree of our national financial operation is improved and the reform is deepened, the range of insurance business has become more and more broad, and the competition of insurers become more fiercely. Thus, for an insurer, it is important to use the premium to invest.Stochastic control is important to portfolio research. In recent years, there has been an increasing attention in the utilization of this theory to insurance related problem. For example, Browne(1995),Hipp and Taksar(2000), Hipp and Plum(2000), Gerber(2004), Yang(2005) apply stochastic optimal control theory to research insurance funds investment. However, these papers all consider that the risky asset is modeled by classical Black-Scholes model, which assume that volatility is only a constant, therefore, this model cannot well describe the actual market volatility's asymmetry. CEV model is a natural extension of Brownian motion. Compared to Black-Scholes model, it assume that the elasticity of variance is a constant, so the volatility is a function of risky asset's price, which offers more practical significance. CEV model is firstly proposed by Cox and Ross(1976).Since then, Cox(1996),Davydov and Linetsky(2001)utilize CEV model to option pricing, and Xiao(2004),Gao(2009) use CEV model to research pension funds management. Currently, CEV model has never been applied to research on insurance funds investment.Through analyzing the above-mentioned articles, this paper pays attention to the utiliza-tion of CEV model to insurance funds investment. This paper consider a model which the risky asset is modeled by CEV model and the aggregate claims are modeled by a Brownian motion with drift. As employment of premium is different from ordinary, which means that the insurer should keep an eye on underwrite risk when he use insurance funds, this paper assume that investment risk has a linear correlation with underwrite risk, according to stochastic control theory, derive the HJB equation related with insurance problem. This equation is non-linear partial differential equation, yet it is difficult to solve it, this paper change primary problem to the dual problem by using Legendre transform. Through setting the parameter values, the op-timal investment strategy for an insurer with CARA or CRRA utility function is presented and the relevant analysis is given, which provides important practical significance for an insurer to invest.