Special Seminar by Prof. Dr. Uwe Schmock

Title: Credit Risk Modelling and Risk Aggregation by Recursive Methods

Speaker: Prof. Dr. Uwe Schmock, Institute for Statistics and Mathematical Methods in Economics, Vienna University of Technology (TU Wien), Austria

Time: 10 February 2023, 13:30-14:30

Room: L-04

Abstract:

The stochastic modelling and aggregation of dependent risks, for example credit risks, is a central risk management task for many financial institutions. We illustrating some basic mathematical challenges and present some modelling approaches involving Bernoulli random variables. We will continue with Poisson approximation and discuss its quality. To combine frequency and severity of losses, we introduce the collective model from actuarial science. If the claim number distribution is of Panjer type, then the extended multivariate Panjer recursion can be used to calculate the distribution of the total loss. To assure numerical stability, we introduce weighted convolutions combined with the Panjer recursion, thereby widening the class of mixture distributions. Time permitting, an implementation will be presented, which is available online.