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Compositions of Conditional Risk Measures and Solvency Capital

Listed author(s):
  • Pierre Devolder

    ()

    (Institut de Statistique, Biostatistique et Sciences Actuarielles, Université catholique de Louvain, Voie du Roman Pays 20 bte L1.04.01, B-1348 Louvain-la-Neuve, Belgium)

  • Adrien Lebègue

    ()

    (Institut de Statistique, Biostatistique et Sciences Actuarielles, Université catholique de Louvain, Voie du Roman Pays 20 bte L1.04.01, B-1348 Louvain-la-Neuve, Belgium)

Registered author(s):

    In this paper, we consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. We first recall the notion of conditional, dynamic and time-consistent risk measures. We link the latter with its iterated property, which gives us a way to construct time-consistent dynamic risk measures from a backward iteration scheme with the composition of conditional risk measures. We then consider particular cases with the conditional version of the value at risk, tail value at risk and conditional expectation measures. We finally give an application of these measures with the determination of the solvency capital of a pension liability, which offers a fixed guaranteed rate without any intermediate cash-flow. We assume that the company is fully hedged against the mortality and underwriting risks.

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    File URL: http://www.mdpi.com/2227-9091/4/4/49/pdf
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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 4 (2016)
    Issue (Month): 4 (December)
    Pages: 1-21

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    Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:49-:d:85319
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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Devolder Pierre & Lebègue Adrien, 2016. "Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances," Dependence Modeling, De Gruyter Open, vol. 4(1), pages 1-22, December.
    3. Cheridito, Patrick & Stadje, Mitja, 2009. "Time-inconsistency of VaR and time-consistent alternatives," Finance Research Letters, Elsevier, vol. 6(1), pages 40-46, March.
    4. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
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