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Risks 2016, 4(4), 49; doi:10.3390/risks4040049

Compositions of Conditional Risk Measures and Solvency Capital

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
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Academic Editor: Luca Regis
Received: 14 November 2016 / Revised: 7 December 2016 / Accepted: 9 December 2016 / Published: 16 December 2016
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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. View Full-Text
Keywords: dynamic risk measures; time consistency; iterated risk measures; pension liability; solvency capital dynamic risk measures; time consistency; iterated risk measures; pension liability; solvency capital
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Devolder, P.; Lebègue, A. Compositions of Conditional Risk Measures and Solvency Capital. Risks 2016, 4, 49.

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