Some Problems Associated With Insurance Company Optimal Investment And Risk Control And Bivariate Mortality Modeling

In this thesis,we studied the problems on optimal investment and risk control problem for an insurer under stochastic factors and density and Copula method for bivariate mortality modeling.In the first subject,the insurer in our model allocates his wealth across a risky asset and a riskless bond where drift,volatility of the risky asset price and the interest rate depend on stochastic factors.In particular,the insurer’s risk process is modeled by a general jump-diffusion risk process while the jumps of the risk process are described as a Poisson random measure with state-dependent jump measure.The aim of the insurer is to maximize the expected utility of the terminal wealth by selecting optimal investment and risk control strategies.We mainly characterize the optimal trading strategy of the risky asset and the risk control strategy for the insurer and investigate existence and uniqueness of classic solutions to the nonlinear HJB PDE under the setting of stochastic factors.Finally we prove the verification theorem based on the classic solution to the HJB PDE.The second subject study the dependence structure of the life statuses,which plays an important role in the valuation of life insurance products involving multiple live for an insurance company.Although the mortality of individuals is well studied in the literature,their dependence remains a challenging field.In this paper,the second objective is to introduce a new approach for analyzing the mortality dependence between two individuals in a couple.It is intended to describe in a dynamic and continuous framework the joint mortality of married couples in terms of marginal female and male mortality rates.The proposed framework is general and aims to capture,by adjusting some parametric form,the desired effect such as the "broken-heart syndrome".To this end,we use a well-suited multiplicative decomposition,which will serve as a building block for the framework and thus will be used to separate the dependence structure from the marginal.Using this decomposition,we make the link with the existing practice and use the density approach introduced recently in the credit risk literature in order to capture the broken-heart syndrome.Finally,given that the framework is general,we propose some illustrative examples and show how the underlying model captures the main stylized facts of bivariate mortality dynamics.Therefore,in this thesis,we investigate a new copula method to study the structure of remaining life of married couples.On the other hand,using the density method which introduced by El Karoui.we consider the(conditional)joint survival probability under different scenarios of life statuses of couple.