Multivariate Actuarial Present Value Under Stochastic Interest Rates

As is known to all, insurance has the function of loss compensation, financing and stabilizing the social function,which is to guard against risks, continue to deepen the reform of the stabilizer and booster. Loss compensation function is the basic function, but also the most distinctive features of the insurance different from other industries. The function of financial intermediation is developed in compensation for the loss function basis and social stability function is the development of the insurance industry to certain degree and depth to the many aspects of social life of an important function. It only after the first two functions can play a role.Insurance has appeared, from originally only has to compensate for the loss function and financing function, development to the present has the function to stabilize the society and the actuarial science playing in the process of development of the insurance role is irreplaceable. Actuarial science is the knowledge and methods of modern probability theory and mathematical statistics, the law of large numbers based on insurance, combined with economics, finance and financial mana gement, and other aspects of professional knowledge, analysis and evaluation of uncertainty of cash flow for the future financial situation of. Therefore, with the development of the insurance industry, the study of actuarial science is catch more and more attention. The majority of the traditional life insurance actuarial theory is one-dimensional and the assumed interest rate is determined, and the purpose is to simplify the calculation. But with the development of economy, the improvement of the government policy, the fluctuation of the international economic environment and other factors can cause the uncertainty of the interest rate.A multi joint function based on the model in this paper is in the life insurance basic knowledge of the theory, combined with stochastic interest rate, and to explore the life insurance actuarial life insurance premiums is calculated. And the traditional binary-dimensional actuarial model is extended to three element model. The first and second chapter mainly introduces the life insurance actuarial knowledge. The third chapter improved the life actuarial function symbols of the commonly used under the assumption of three element life model. The fourth chapter in the third chapter based on the combination of random interest ra tes, mainly discusses the stochastic interest rate of family life insurance actuarial premium, and the fifth chapter mainly writes the doubly stochastic interest rate of life insurance model. Finally, the chapter gives the Markov process of ternary combined life insurance model.