Research On The Optimal Investment Strategy Under The CEV Model

With the improvement of China's policies in recent years,the investment and reinsur-ance problems of insurance companies have become the focus of research.In the insurance market,insurance companies not only rely on collecting premiums to maintain the operation of the compaty,but also buy reinsurance to reduce the risks and otain the greatest profits by investment.In the current insurance financial market,more and more competitive appear because of the increase of the number of insurance company.It is more and more difficult for insurance companies to maintain their operations only by earning premiums.To cope with this problem,insurance companies have taken several measures to maintain their operations.On the one hand,reinsurance measures are usually adopted to reduce the risks of insurance companies in their daily operations.On the other hand,insurance companies also usually invested in capital markets to make greater profits.With the rapid development of China's economy,insurance companies have a deeper understanding of the reinsurance industry and more options for investment.The wealth process of the insurance companies is described in this thesis and it follows a compound Poisson process with jump diffusion,a certain proportion of reinsurance can be purchased.Both insurance companies and reinsurance companies are allowed to invest in the risk-free asset and the risky asset,in which the price process of the risky asset is described by the CEV model.In addition,we believe that there is a certain correlation between the risky asset and the risky asset.Under the effect of the risk-free asset and dual the risky asset.The purpose of this paper is to maximize the expected utility of the terminal wealth of the insurance company.Through a series of methods,the closed-form solution of maximizing the exponential utility function is obtained under some assumptions.Then the optimal investment reinsurance strategy is deduced according to the form of the solution.Compared with Wang et al(2017),Insurance company in this paper invests in risk-free investment and double risk investment,in which the process of double risk investment is subject to CEV model.The innovation lies in that this paper can deal with risk investment,dividing the funds used for risk investment into two parts,and investing in two different CEV models respectively.In addition.Our aim is to maximize the expected utility of the terminal wealth of the original insurance company.By solving the corresponding HJB equation,using Legendre transformation and duality theory,we can obtain the explicit solution that maximizes the exponential utility under some assumptions.This thesis is arranged as follows:firstly,in the first chapter,it introduces the histo-ry and the relevant knowledge background of investment and reinsurance,and it gives the utility function,the form of proportional reinsurance,and the explanation of premium prin-ciple.In the second chapter,we can deduce the wealth process of the insurance company by introducing the model formula.By applying the stochastic control theory,we get the corresponding HJB equation according to the relevant,background knowledge.Then,in the third chapter,we deduce three optimal reinsurance strategies through a series of transformations and simplifications of the HJB equation.By using Legendre transform and dual theory,we deduce the optimal reinsurance strategy according to the form of the solution.In the fourth chapter,the corresponding summary and induction are given.