Insurance Surplus Mathematics

The analysis of the development over time of the surplus on a portfolio of insurance business is considered. The classical Poisson and Sparre Andersen risk models are studied. Unified treatment of moments and distributions of quantities related to the event of ruin is done through a discounted penalty function approach. Random variables of interest include the time of ruin itself, the deficit immediately after ruin occurs, and the surplus immediately prior to ruin. Defective renewal equations and Laplace transforms are utilized extensively. Prerequisites are familiarity with aggregate loss models at the level of ActSc 431/831 or equivalent.