Title: Recursive Methods for the Aggregation of Dependent Risks with a View towards Numerical Stability

Speaker: Prof. Dr. Uwe Schmock of Vienna University of Technology (TU Wien) in Austria

Abstract: 

The stochastic modelling and aggregation of dependent risks is a central risk management task for many financial institutions. After an introduction illustrating some basic mathematical challenges, we will review Poisson approximation, the collective model from actuarial science, Panjer distributions, and the extended multivariate Panjer recursion. To assure numerical stability, we introduce weighted convolutions combined with the Panjer recursion, thereby widening the class of mixture distributions. The aim is to discuss a multi-business-line variant of the collective model, mixed by a convex combination of non-negative (mainly unbounded) claim number intensities to obtain an arbitrary linear dependence structure -- and still use recursive methods to calculate the loss distribution of the portfolio. Time permitting, an implementation will be presented, which is available online.