On stochastic difference equations in insurance ruin theory

Abstract

We study the insurance ruin problem in a model where in addition to the basic insurance business, the company operates in the general financial market. The development of the capital is described as the solution to a stochastic difference equation. Basic estimates for ruin probabilities are recalled from the literature and qualitative descriptions of the range and the limit of the capital are given.

Keywords:

• stochastic difference equation
• ruin probability
• investment

AMS 2000 Subject Classifications::

• Primary 60G40
• Secondary 39A50