An application of stochastic interest rate models in life assurance
Although assurance companies are pooling many risks, the law of large numbers does not fully apply. This leaves the companies with a possibility of insolvency and a corresponding need for contingency reserves which are matters of serious concern. In this thesis we derive some fundamental results that are useful when the time comes to set contingency reserves or to assess solvency. We use a model where both the mortality and the interest rates are random variables. We choose to model the force of interest by the Ornstein-Uhlenbeck process. For temporary assurances and endowment assurances we derive an efficient recursive method to find the first three moments of the present value of a portfolio of identical policies. We then use these moments to approximate accurately the distribution of the present value of such a portfolio, firstly when the number of policies in the portfolio tends to infinity, and secondly, for a portfolio of finite size.