Mathematical Tools in Risk Management

In this talk I will begin by giving a short overview of the active modelling areas within large banks. I will then focus on the construction of multivariate distributions using models for the univariate marginals and a dependence structure phrased in the language of copulas. I will shortly discuss models for the marginals but in particular discuss copula properties and their implications on value at risk calculations and stress testing. I will also shortly mention further applications of copulas to for instance the pricing of credit derivatives. In the end of my talk I will discuss the use of Fourier transform methods and the method of stationary phase in the analysis of the tail of the profit and loss distribution for a large portfolio containing non-linear contracts.