Optimal Behavior Investment Strategy Under The Wealth Constraint For Insurance Companies In Lévy Market

After the insurance companies are allowed to invest in the capital market,the total assets of the insurance companies are increasing every year,while the rate of return is low and the allocation of the investment assets is unreasonable.Insurance companies are paying more and more attention to the content of optimal investment and capital safety and increase revenue and improve competitiveness in the market.Therefore,it is of great practical significance to analyze the optimal investment quota on each asset under the premise of ensuring the normal operation of the insurance company.The traditional portfolio theory is based on the theory of expected utility maximization.However,the complex market environment and its own psychological factors make this theory do not conform to the reality,and the theory of utility maximization is being questioned more and more.Later,a series of theories that make up the maximization of expected utility appear.The most famous theory in these theories is cumulative prospect theory.The cumulative prospect assumes that profit and loss are relative to the reference point.In the case of the same profit and loss,the loss gives a greater psychological sense to the investor,which is more consistent with the reality.Based on this,this paper assumes that insurance companies are loss averse when making investment decisions.First of all,in the both cases of the no limit of the wealth base and the limit of the wealth base,it is assumed that the capital of the insurance company is invested in a riskless asset and n risk assets.Because of the various uncertain factors in the market,the price of the risk assets will fluctuate,that is,it can not be described in a continuous process.Therefore,this paper assumes that the risk assets are subject to the Lévy distribution.Secondly,we assume that the insurance surplus process is a classical Lundber-Cramér model.Finally,the safety and liquidity problems of insurance companies are added to the model.A minimum safety limit is set for the final wealth value to ensure that the insurance company can operate normally under the condition of a bad market.The goal of an insurance company is to maximize the expected utility when the final wealth exceeds his expectation level.The solution process is divided into two steps.The first step is to find the discount factor,and use martingale method to make the dynamic problem into a static problem,so that it can be easily solved.The second step is to use Lagrange method to find out analytic expression of the optimal investment strategy and the optimal wealth.The method of numerical simulation is used to discuss the influence of the volatility and yield of risk assets,the amount of insurance company,the reference point and the optimal wealth process on the optimal investment strategy,and compare the optimal investment strategy and the final wealth value in two cases of with and without wealth constraints.