Catastrophe Risk and Insurer Solvency: A Diffusion-Jump Analysis - Powers, Michael R.; Ren, Jiandong (Assurances et gestion des risques / Insurance and Risk Management, 2003)
In recent years, the magnitudes of realized catastrophe (extreme-event) losses have increased dramatically. The effects of increasing catastrophe risks on the insurance industry have been profound. In the current private insurance market, the possibility of insurer default is of great concern to insurers and their investors. However, there is limited actuarial or financial theory for analyzing catastrophe insurance contracts based upon the probability of ruin. In this article, we develop a mixed diffusion and compound Poisson jump model of insurer net worth to reflect the fact that insurers are faced with both non-catastrophe and catastrophe risks. Under the assumption of exponentially distributed catastrophe losses, we derive analytical approximations to the insurer ruin probability. Assuming constant catastrophe loss amounts, we calculate the ruin probability numerically and compare the results with those for exponentially distributed losses.