Analysis of the insurer's surplus and related quantities

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Sound financial risk management requires that the insurer examine the possibility of adverse claims experience on a given block of insurance business. The nature of such examination necessitates the use of detailed mathematical models to provide a view of the potential claims experience of this business. In particular, techniques from applied probability may be applied to quantify the possibility that 'ruin' occurs, i.e. that the insurer has insufficient capital to meet these claim liabilities at any juncture. Furthermore, this approach may also be used to provide insight into the nature of the events leading up to ruin. Mathematical advances in the last decade have allowed for a systematic quantitative analysis of the time at which ruin may be expected to occur, the funds which are available to the insurer for claims payments when this happens, the nature of the claims which cause this to happen, and the resultant shortfall faced by the insurer. Moreover, powerful computational resources are now available which permit the use of more realistic mathematical models which are of necessity more complex than those previously considered. The purpose of the proposed research is to examine such complex models with a view to the examination of the analysis of the insurer's funds leading up to ruin and the nature of such ruin itself. Such analysis now appears to be possible in light of the wide variety of mathematical tools which are now available.