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VALUATION OF HYBRID FINANCIAL AND ACTUARIAL PRODUCTS IN LIFE INSURANCE BY A NOVEL THREE-STEP METHOD

Published online by Cambridge University Press:  14 August 2020

Griselda Deelstra
Affiliation:
Department of Mathematics Université libre de Bruxelles Boulevard du Triomphe, 1050 Brussels, Belgium
Pierre Devolder
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA/LIDAM) Université Catholique de Louvain 20 Voie du Roman Pays, 1348 Louvain la Neuve, Belgium
Kossi Gnameho
Affiliation:
Department of Mathematics Université libre de Bruxelles Boulevard du Triomphe, 1050 Brussels, Belgium
Peter Hieber*
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA/LIDAM) Université Catholique de Louvain 20 Voie du Roman Pays, 1348 Louvain la Neuve, Belgium Institute of Insurance Science University of Ulm Helmholtzstr. 20, 89069 Ulm, Germany E-Mail: peter.hieber@uni-ulm.de
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Abstract

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Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel three-step projection algorithm to valuate hybrid contracts by decomposing their payoff in three parts: a financial, hedgeable part, a diversifiable actuarial part, and a residual part that is neither hedgeable nor diversifiable. The first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2020 by Astin Bulletin. All rights reserved

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