Decomposing Dynamic Risks into Risk Components

References

• Barbarin J (2008) Valuation, hedging and the risk management of insurance contracts. Doctoral thesis, Université Catholique de Louvain, Ottignies-Louvain-la-Neuve, Belgium.Google Scholar
• Bauer D, Zanjani G (2013) Capital allocation and its discontents. Dionne G, ed. Handbook of Insurance, 2nd ed. (Springer, New York), 627–645.Crossref, Google Scholar
• Bauer D, Kling A, Ruß J (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. Astin Bull. 38(2):621–651.Crossref, Google Scholar
• Baucells M, Borgonovo E (2013) Invariant probabilistic sensitivity analysis. Management Sci. 59(11):2536–2549.Link, Google Scholar
• Biagini F, Schreiber I (2013) Risk-minimization for life insurance liabilities. SIAM J. Financial Math. 4(1):243–264.Crossref, Google Scholar
• Biagini F, Rheinländer T, Schreiber I (2016) Risk-minimization for life insurance liabilities with basis risk. Math. Financial Econom. 10(2):151–178.Crossref, Google Scholar
• Biagini F, Rheinländer T, Widenmann J (2013) Hedging mortality claims with longevity bonds. Astin Bull. 43(2):123–157.Crossref, Google Scholar
• Biffis E (2005) Affine processes for dynamic mortality and actuarial valuations. Insurance Math. Econom. 37(3):443–468.Crossref, Google Scholar
• Biffis E, Denuit M, Devolder P (2010) Stochastic mortality under measure changes. Scandinavian Actuarial J. 2010(4):284–311.Crossref, Google Scholar
• Borgonovo E (2011) Sensitivity analysis in decision making. Cochran JJ, Cox LA Jr, Keskinocak P, Kharoufeh JP, Smith JC, eds. Wiley Encyclopedia of Operations Research and Management Science (Wiley, New York), 1–11.Google Scholar
• Borgonovo E, Plischke E (2016) Sensitivity analysis: A review of recent advances. Eur. J. Oper. Res. 248(3):869–887.Crossref, Google Scholar
• Borgonovo E, Hazen GB, Plischke E (2016) A common rationale for global sensitivity measures and their estimation. Risk Anal. 36(10):1871–1895.Crossref, Google Scholar
• Bühlmann H (2000) Life insurance with stochastic interest rates. Ottaviani G, ed. Financial Risk in Insurance (Springer, Berlin), 1–24.Crossref, Google Scholar
• CEIOPS (2010) QIS 5 technical specifications (Committee of European Insurance and Occupational Pensions Supervisors, Frankfurt, Germany). Accessed November 22, 2019, https://eiopa.europa.eu/Publications/QIS/QIS5-technical_specifications_20100706.pdf.Google Scholar
• Christiansen MC (2007) A joint analysis of financial and biometrical risks in life insurance. Doctoral thesis, Universität Rostock, Rostock, Germany.Google Scholar
• Christiansen MC (2013) Safety margins for unsystematic biometric risk in life and health insurance. Scandanavian Actuarial J. 2013(4):286–323.Crossref, Google Scholar
• Christiansen MC, Helwich M (2008) Some further ideas concerning the interaction between insurance and investment risks. Blatter DGVFM 29(2):253–266.Crossref, Google Scholar
• Dahl M, Møller T (2006) Valuation and hedging of life insurance liabilities with systematic mortality risk. Insurance Math. Econom. 39(2):193–217.Crossref, Google Scholar
• Dahl M, Melchior M, Møller T (2008) On systematic mortality risk and risk-minimization with survivor swaps. Scandinavian Actuarial J. 2008(2-3):114–146.Crossref, Google Scholar
• Di Nunno G, Øksendal B, Proske F (2009) Malliavin Calculus for Lévy Processes with Applications to Finance (Springer, Berlin).Crossref, Google Scholar
• Efron B, Stein C (1981) The jackknife estimate of variance. Ann. Statist. 9(3):586–596.Crossref, Google Scholar
• Fischer T (2004) On the decomposition of risk in life insurance. Working paper, Technische Universität Darmstadt, Darmstadt, Germany.Google Scholar
• Fu MC, Hong LJ, Hu J-Q (2009) Conditional Monte Carlo estimation of quantile sensitivities. Management Sci. 55(12):2019–2027.Link, Google Scholar
• Gatzert N, Wesker H (2014) Mortality risk and its effect on shortfall and risk management in life insurance. J. Risk Insurance 81(1):57–90.Crossref, Google Scholar
• Hájek J (1968) Asymptotic normality of simple linear rank statistics under alternatives. Ann. Math. Statist. 39(2):325–346.Crossref, Google Scholar
• Hoeffding W (1948) A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19(3):293–325.Crossref, Google Scholar
• Hoem JM (1988) The versatility of the Markov chain as a tool in the mathematics of life insurance. Trans. 23rd Internat. Congress Actuaries (International Actuarial Association, Ottawa), 171–202.Google Scholar
• Hong LJ (2009) Estimating quantile sensitivities. Oper. Res. 57(1):1118–1130.Link, Google Scholar
• Insurance Information Institute (2017) Facts + Statistics: Industry overview. Accessed February 27, 2019, http://www.iii.org/fact-statistic/industry-overview.Google Scholar
• Jeanblanc M, Rutkowski M (2000) Modelling of default risk: An overview. Yong J, Cont R, eds. Mathematical Finance: Theory and Practice (Higher Education Press, Beijing), 171–269.Google Scholar
• Jetses J (2018) Martingalzerlegung von Verbindlichkeiten in der Personenversicherung. Master’s thesis, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany.Google Scholar
• Karabey U, Kleinow T, Cairns AJ (2014) Factor risk quantification in annuity models. Insurance Math. Econom. 58:34–45.Crossref, Google Scholar
• Kochanski M, Karnarski B (2011) Solvency capital requirement for hybrid products. Eur. Actuarial J. 1(2):173–198.Crossref, Google Scholar
• Liu G (2015) Simulating risk contributions of credit portfolios. Oper. Res. 63(1):104–121.Link, Google Scholar
• Martin R, Tasche D (2007) Shortfall: A tail of two parts. Risk 20(2):84–89.Google Scholar
• Møller T (2001) Risk-minimizing hedging strategies for insurance payment processes. Finance Stochastics 5(4):419–446.Crossref, Google Scholar
• Nualart D (2006) The Malliavin Calculus and Related Topics (Springer, Berlin).Google Scholar
• Saltelli A, Tarantola S (2002) On the relative importance of input factors in mathematical models: Safety assessment for nuclear waste disposal. J. Amer. Statist. Assoc. 97(45):702–709.Crossref, Google Scholar
• Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global Sensitivity Analysis: The Primer (John Wiley & Sons, New York).Google Scholar
• Schilling K (2017) Comparing financial and biometric risks in annuity conversion options via the MRT decomposition. Working paper, Universität Ulm, Ulm, Germany.Google Scholar
• Sobol IM (1993) Sensitivity estimates for nonlinear mathematical models. Math. Modelling Comput. Exp. 1:407–414.Google Scholar
• Rosen D, Saunders D (2010) Risk factor contributions in portfolio credit risk models. J. Banking Finance 34(2):336–349.Crossref, Google Scholar
• Wagner HM (1995) Global sensitivity analysis. Oper. Res. 43(6):948–969.Link, Google Scholar