A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives

Christophette Blanchet-Scalliet (), Diana Dorobantu and Yahia Salhi ()
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Christophette Blanchet-Scalliet: PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique
Diana Dorobantu: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Yahia Salhi: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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Abstract: In this paper, we study the pricing of life insurance portfolios in the presence of dependent lives. We assume that an insurer with an initial exposure to n mortality-contingent contracts wanted to acquire a second portfolio constituted of m individuals. The policyhold-ers' lifetimes in these portfolios are correlated with a Farlie-Gumbel-Morgenstern (FGM) copula, which induces a dependency between the two portfolios. In this setting, we compute the indifference price charged by the insurer endowed with an exponential utility. The optimal price is characterized as a solution to a backward differential equation (BSDE). The latter can be decomposed into (n − 1)n! auxiliary BSDEs. In this general case, the derivation of the indifference price is computationally infeasible. Therefore, while focusing on the example of death benefit contracts, we develop a model point based approach in order to ease the computation of the price. It consists on replacing each portfolio with a single policyholder that replicates some risk metrics of interest. Also, the two representative agents should adequately reproduce the observed dependency between the initial portfolios.

Keywords: representative contract; life insurance; utility maximization; indifference pricing (search for similar items in EconPapers)
Date: 2019
New Economics Papers: this item is included in nep-ias, nep-rmg and nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-01258645v1
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Citations: View citations in EconPapers (2)

Published in Methodology and Computing in Applied Probability, 2019, 21 (423-448), ⟨10.1007/s11009-017-9611-2⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01258645

DOI: 10.1007/s11009-017-9611-2

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