Prospective Reserves of Life Insurance Policies under the Heath-Jarrow-Morton Framework

Abstract

In this thesis we consider a general stochastic interest rate under the HJM (Heath-Jarrow-Morton) framework. We further present a general model for the pricing of life insurance policies allowing for a wider range of stochastic policy functions than previously done within the HJM framework. This is carried out by modelling them under a general financial market model with Gaussian noise. Furthermore, we develop standard pricing formulas based on financial arbitrage methods for both current time and future time-points. It is worth noting that these equations are contingent on formulas pricing the instantaneous values of the policy functions as financial claims. Lastly, we give an example where the theory is applied to exactly evaluate the price of reserves within a new theoretical pension scheme with stochastic policy functions tied to the interest rate. As a part of this example we develop small generalizations of some financial pricing formulas for call and digital options on zero-coupon bonds. In order to rigorously justify these results the thesis covers a large amount of background material. This includes measure and probability theory, as well as using these to introduce important concepts in interest rate, finance and classical insurance theory.