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Compositions of Conditional Risk Measures and Solvency Capital

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  • 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)

Abstract

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.

Suggested Citation

  • Pierre Devolder & Adrien Lebègue, 2016. "Compositions of Conditional Risk Measures and Solvency Capital," Risks, MDPI, vol. 4(4), pages 1-21, December.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:49-:d:85319
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    References listed on IDEAS

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