Matrix And Its Application In Combined Life Insurance

Usually the traditional actuarial theory is based on a fix interest rate with a purpose to simplify calculations.However,since the life insurance is a long-term economic action,the factors of government policy and economic cycles may cause the interest rate to be uncertain during the time of insurance,the study on actu-arial theory and method under random rates of interest has become an important and popular topic.It appears that formulas for the moments of the present value of the benefits are quite extensive,especially for the discrete-time case.So this paper derives the matrix form for the first two moments of the present value of the benefits from combined life insurance in a stochastic interest environment. We can simplify the expressions for the appropriate moments.Moreover,matrix notation not only makes calculations easier,but also provides a nice form for some important equations,for example equivalence principle.It is divided into seven chapters:In chapter 1,We give introductions to the development and research of life insurance actuarial theory under random interest rate and our research object.In chapter 2,We give the essential definitions.In chapter 3,After a breif description of the present value of cumulative payment streams generated by combined life insurance contract,we give expressions for the first two moments about a single policy and a general portfolio.In chapter 4,our main results:the matrix form of the first two moments of Z and Z_N.In chapter 5,we establish the model for the stochastic interest by a Wiener and an Ornstein-Uhlenbeck process and a numerical illustration for the rate of interest modeled by a Wiener process is provided.In chapter 6 and 7,we give the detailed proofs and prospect.