Mathematical finance has developed over the past 10 years, say, into a field of mathematics (stochastics) interesting in its own right. Mainly born out of the need for pricing and hedging more complicated derivatives, the field has reached a scientific maturity acknowledged by practitioners and academics alike. Over the last couple of years, various more applied issues from the realm of Integrated Risk Management have come to the forefront. I am thinking of issues like the construction of good measures of risk, the analysis of a reliable stress scenario methodology, a critical discussion of capital allocation rules, the merger at the quantitative level of different types of risk within a bank (market, credit, operational) and between banking and insurance (combining typically long term underwriting risk with short term investment risk, say). New important risk management tools like Dynamic Financial Analysis, and Embedded Value are entering the (insurance) market. In this talk, I will highlight some of the statistical modelling issues underlying the above developments. Key elements will be: -- the use of extreme value theory for measuring risk beyond VaR, and -- the use of copula--techniques for modelling dependence beyond linear correlation. Various examples will be given.
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