Lévy processes in actuarial ruin theory and exotic option pricing

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The recent turmoil in financial markets, triggered by defaults in various countries, has shed new lights on the importance of risk measurement for maintaining adequate capital requirements and efficiently pricing financial products. A comprehensive framework for implementing procedures to identify, measure, and analyze risk has been developed in most industrialized countries. Actuarial ruin theory aims at modelling, and measuring the risk of, the wealth of an insurance company. Very similarly, structural models in credit risk are interested in the solvency of firms and financial institutions. On the other hand, it has been acknowledged by practitioners and academics that simple stochastic models for the price of financial assets can not explain empirical facts observed on the markets. At the same time, the complexity of financial derivatives written on those assets is constantly increasing. In all cases, there is a need for sophisticated financial models and powerful mathematical techniques designed for risk measurement and for the pricing and hedging of financial instruments. This research program focuses on the interactions between probability and stochastic processes, with actuarial science and finance. Problems arising in actuarial science and finance generate innovative research in the theory of probability and stochastic processes. On the other hand, the analysis of models of interest for actuaries and investment bankers requires a good knowledge of the mathematics used in the underlying model. It is expected that new analytic and probabilistic mathematical techniques will be developed to perform the analyses alluded to above.