Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends

Abstract

In this thesis, we consider a risk model which incorporates multiple threshold levels characterizing an insurer's minimal capital requirement, dividend paying situations, and external financial activities. Our model is based on discrete monetary and time units, and the main quantities of interest are the finite-time ruin probabilities and the expected total discounted dividends paid prior to ruin. We mainly focus on the development of computational methods to attain these quantities of interest. One of the popular methods in the current literature used for studying such problems involves a recursive approach which incorporates appropriate conditioning arguments on the claim times and sizes, and we implement this procedure as well. Furthermore, ruin can occur due to both a claim as well as interest expense accumulation as our model allows the insurer to borrow money from an external fund. In this thesis, we consider only non-stochastic interest rates for both lending and borrowing activities. After constructing appropriate recursive formulae for the finite-time ruin probabilities and the expected total discounted dividends paid prior to ruin, we investigate various numerical examples and make some observations concerning the impact our threshold levels have on finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.