ISBN 978-3-8439-1783-4

978-3-8439-1783-4, Reihe Mathematik

Martin Hampel
Three Mathematical Explorations in Connection with the Non-Life Sub-Module of Solvency II SCR-Formula, Tractable Customer Base Process, VaR Estimate

141 Seiten, Dissertation Carl von Ossietzky Universität Oldenburg (2014), Softcover, B5

Zusammenfassung / Abstract

When Solvency II takes effect, every European insurance company is obligated to apply a standard approach for its Solvency Capital Requirement (SCR) calculation unless an internal risk model has been legitimated by the corresponding national authority. Additionally, all companies have to provide Own Risk and Solvency Assessments (ORSA). This thesis deals with three aspects of the stand-alone SCR formula for the premium and reserve risk of the non-life risk sub-module of the standard approach. At first, a bias in the SCR calculation is pointed out and a correction formula is derived. Next, a Markov chain as stochastic customer base model is presented which potentially meets the trade-off between mathematical appropriateness and manageability in application. Mathematical operatives may benefit from such a handy model if it is applied to determine the so-called Volume Measure of the standard formula or, also, if it is used for the obligatory ORSA process. Typical asymptotic properties are examined. Finally, this thesis derives the Mean Squared Error of the Value-at-Risk estimate for a lognormal risk in a first step analysis as the Value-at-Risk estimate is an important component to determine the company’s individual SCR.