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

Author

Listed:
  • 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

    (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)

  • Yahia Salhi

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

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.

Suggested Citation

  • Christophette Blanchet-Scalliet & Diana Dorobantu & Yahia Salhi, 2019. "A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives," Post-Print hal-01258645, HAL.
    • Handle: RePEc:hal:journl:hal-01258645
    DOI: 10.1007/s11009-017-9611-2
    Note: View the original document on HAL open archive server: https://hal.science/hal-01258645
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    References listed on IDEAS

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    Cited by:

    1. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.
    2. Ying Jiao & Yahia Salhi & Shihua Wang, 2022. "Dynamic Bivariate Mortality Modelling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 917-938, June.

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    Keywords

    representative contract; life insurance; utility maximization; indifference pricing;
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