Ruin probabilities

Abstract

The study of ruin probabilities was largely initiated in Sweden in the first half of the century. Some of the main general ideas were laid down by Lundberg [24], while the first mathematically substantial results were given in Cramer [10]. It is widely believed that the thinking promoted by ruin theory is extremely important for modern risk management in insurance. In addition, ruin theory has fruitful methodological links and applications to other fields of applied probability, like queueing theory and mathematical finance. This dissertation focuses on methods of tackling the problem of calculating the ruin probability for some specific risk models, mainly the compound Poisson model and the renewal model. The ideal result for the actuary is that of a closed-form solution so that ruin probability could be easily calculated, and hence the decision making process could work out smoothly. However, this is not always the case. In this dissertation, we shall consider specific examples of models whose closed-form ruin probability is known and for other models where closed-form solution is not possible we use illustrative examples together with numerical analysis, approximations and bounds as alternatives to solve this problem. Other alternatives to the ones considered in this thesis are also suggested.