Present value of some insurance portfolios

Abstract

In this paper we introduce some general theorems of Poisson processes and use them to study the first two moments of the present value of an insurance portfolio. We allow for several handling times of claims and also allow the discounting process to be stochastic, in particular we let it follow a geometric Brownian motion and the Cox, Ingersoll, and Ross (LIR) model. We also give a brief discussion of the problem of finding the distribution function of the present value. Examples are given to illuminate the general theory, showing that although sometimes complicated, actual computations are often possible.

Key words:

• Poisson processes
• moments of present value
• distribution of present value
• stochastic discounting