A Study On Optimal Investment And Reinsurance Strategies For An Insurer Within Stochastic Interest Rate Framework

As the development of finance and insurance markets,risk management has been identified and recognized as an important part of modern financial investment and insurance mathematics.Financial risk management is the practice of creating economic value in a firm by using financial instruments to manage exposure to risk due to the fact that financial risk management can be qualitative and quantitative.Financial risk management focuses on when and how to hedge the risk using financial instruments.Investment theory contains the body of knowledge used to support the decisionmaking process of choosing investment for various purpose.Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk,or minimize risk for a given level expected return,by choosing the proportions of various assets.The study on investment and reinsurance for an insurer combine the financial investment and reinsurance business,facilitating the stable development of insurance industry.My dissertation is mainly devoted to the following two aspects for an insurer:Firstly,we will consider the optimal investment and reinsurance problem under the criterion of maximizing expected utility of the terminal wealth in stochastic enviroment.Secondly,we formulate and introduce the behavioral economics theory(loss aversion utility)into the stochastic model.Meanwhile,we will try to give the very explicit expressions of optimal solutions to make the model and the problem considered more practical.In the process of operating insurance company,we consider the insurer investing in the financial market as well as purchasing proportional reinsurance to spread risk.Due to the duration of investment,it is natural to take stochastic interest rate into consideration.Then,section 2 considers the optimal investment and proportional strategies for an insurer under stochastic interest rate where we introduce Heston'SV model to describe stock price.Section 3 adopts the loss aversion(S-shaped)utility function which is within the framework of prospect theory to describe an insurer's preference under within stochastic interest model.The recent literature on behavioural finance have provided that the prospect theory corresponds better with how economic agents actually behave in real world risk situations.My dissertation would be devoted to formulating the models to solve optimal investment problem,optimal reinsurance strategy as to standard optimisation paradigm,expected utility maximization and behavioral portfolio selection problem via stochastic dynamic programming method and martingale method.Some numerical examples are presented to illustrate our strategies.