Optimal Control Strategies Of Two Kinds Of Insurance Companies In Stochastic Environment

Insurance plays an important role in individual's or company's economic behav-iors.It can help reduce individual's risks efficiently.How to manage the insurance pre-miums and invest is an important issue for a insurance company.Based on the objects of insurance,this thesis investigates the optimal control strategies for a life insurance and pension plan insurance company.Unfortunately,in most of the existing researches,the model of the insurance company is not realist.They do not consider more complex stochastic environments and investment preferences.This thesis establishes more rea-sonable and realist models for the life insurance and pension plan insurance company.Then,martingale method and dynamic programming method are applied to derive the optimal strategies.In order to obtain more efficient models for insurance companies,this thesis is divided into four parts.In the first part,we study the optimal reinsurance and in-vestment strategies for an insurer under interest rate and inflation risks.Firstly,we introduce auxiliary processes to transform the original optimization problem into a self-financing problem.Then,stochastic dynamic programming method is employed to derive the optimal strategies under CRRA utility maximization.The second part studies the portfolio selection for a DC pension fund.Two optimization rules are con-sidered:loss aversion and VaR constraint.In order to derive the optimal strategies,martingale method is applied.This part also compares the optimal strategies under these two optimization rules.The third part investigates the optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework.The goal of the pension fund manager is to maximize the expectation of the CRRA utility of terminal value over the guarantee at retirement.Auxiliary processes are introduced and stochastic dynamic programming method is used to obtain the closed forms of the investment strategies.In the fourth part,the management of DC pension plan under stochastic interest rate and mean-reverting returns is studied.The pension manager should maximize the expected terminal value and minimize the variance of terminal value.We firstly transform it into a one-objective optimization problem by Lagrange dual theory,then use the dynamic programming method to obtain the efficient frontier and efficient strategies.Furthermore,in each part,this thesis uses Monte Carlo Meth-ods(MCM)to present the sensitivity analysis to show the economic behaviors of the insurance companies.Besides,the sensitivity analysis shows the compact of economic parameters on the optimal strategies and verifies that the financial models in this thesis are reasonable and efficient.The problems in this thesis study the optimal control strategies for an insurance company under stochastic environment and different optimization rules.Solving them requires the theories of stochastic calculus,martingale method,dynamic programming method.Besides,for non self-financing problems,we need to transform them into self-financing problems.The solving procedures have important inspirations for similar problems.Moreover,the conclusions of this thesis can provide efficient suggestions for the economic behavior of an insurance company.