An Analysis On Insurer's Optimal Investment Behavior

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.In this paper,author establish insurance investment model on continuous time and discrete-time respectively.The classical portfolio theory and its disadvantages are introduced here,and the robust optimization that is to overcome theses deficiencies of is expounded.Robust optimization has been applied to model portfolio selection problems in order to describe the uncertainty of the market and to alleviate the sensitivity of optimal portfolios to statistical errors in the estimations of problem parameters.The insurance investment under real market environment is studied.By applying the robust optimization,this paper establish the robust insurance investment model. A robust factor model is developed for the asset returns,and the parameters are supposed to perturb in a "joint" ellipsoidal uncertainty set proposed by Lu(2006).Suppose the insurer's utility function is exponential,then maximizing the expected utility is equivalent to a robust portfolio selection problem containing expectation,variance and covariance.It is further shown that the robust insurance investment model can be reformulated as a cone programming problem with SDP and SOCP constraints and thus can be computed.When the price of the risky asset is described by the Black-Scholes market model,another optimal investment strategy is considered.By assuming the number of the claims follow a compound Poisson distribution,the underwrite risk is considered.This analysis is different from the traditional study of premium investment.Thus the expression of the optimum investment proportion involves some variables such as the number of policy-holders and so on,which offers more practical significance.The relations between the optimum proportion and some variables such as the number of policy-holders is studied simultaneously.The results is general and it provides more theoretical and practical significance for the insurer to invest with premium and change investment according to the economic environment.