A joint analysis of financial and biometrical risks in life insurance [Elektronische Ressource] / vorgelegt von Marcus Christian Christiansen

A joint analysis of nancial andbiometrical risks in life insuranceMarcus C. ChristiansenA joint analysis of nancial and biometricalrisks in life insuranceDissertationzurErlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)der Mathematisch-Naturwissenschaftlichen Fakult atder Universit at Rostockvorgelegt vonMarcus Christian Christiansengeboren am 13. Oktober 1978 in Michigan (Vereinigte Staaten)1. Gutachter: Prof. Dr. Hartmut Milbrodt, Universit at Rostock2.hter: Prof. Dr. Holger Drees, Universit at Hamburg3. Gutachter: PD Dr. Ulrich Orbanz, Towers Perrin TillinghastTag der Verteidigung: 17. Januar 2007ContentsIntroduction 71 Financial and biometrical risks in life insurance 111.1 Classi cation of risks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Life insurance model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Expanded life insurance model . . . . . . . . . . . . . . . . . . . . . . 161.4 Decomposition of risk . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 A sensitivity analysis approach for functionals on speci c function spaces 252.1 A gradient vector for functionals on L () . . . . . . . . . . . . . . . . 26p2.2 A gradient vector for on BV . . . . . . . . . . . . . . . . 28 2.3 Comparison with concepts of the statistical literature . . . . . . . . . . 31d2.4 An extended gradient vector for L ()-functionals . . . . . . . . . . . 33pd2.5 Anedt vector for BV -functionals . . .