Importance Sampling Methods for a Motor Portfolio

Specialeforsvar ved Emil Krarup Hatt

Titel: Importance Sampling Methods for a Motor Portfolio 

Abstract: This thesis seeks to empirically estimate \textit{Value-at-Risk} and Expected Shortfall in an automobile insurance portfolio. Prior to estimation, a special attention is given to time series methods in particular in estimating seasonal patterns and an underlying trend of the data. Finally, the classical Importance Sampling theory is extended to quantiles following recent work by Glynn. The risk measures are related to large losses and therefore Importance Sampling is used to reduce variance in the numerical estimates where special attention is given to the heavy-tailed liability losses. A one-period model for Expected Shortfall is analysed as a benchmark study, and from there the methods are extended to a multi-period setup. In the latter, Glynn's article serves as inspi-ration for estimating Value-at-Risk which is ultimately transferred to the Expected Shortfall. The main result of the thesis is a generic method of how to estimate Expected Shortfall for a sum of random variables whose distribution is in the Max-domain of Attraction of the Frechét distribution. Also, a closed form solution for the shift parameter theta for the Importance Sampling algorithm is derived

Vejleder:  Jeffrey Collamore
Censor:    Mette Havning