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

Author

Listed:
  • Christophette Blanchet-Scalliet

    (Institut Camille Jordan Université de Lyon CNRS UMR 5208)

  • Diana Dorobantu

    (University of Lyon, UCBL, LSAF EA2429)

  • Yahia Salhi

    (University of Lyon, UCBL, LSAF EA2429)

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 contracts. The policyholders’ 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 indifference price is characterized as a solution to a backward stochastic differential equation (BSDE), which 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 contracts should adequately reproduce the observed dependency between the initial portfolios. We implement the proposed procedure and compare the computed prices to classical valuation approach.

Suggested Citation

  • Christophette Blanchet-Scalliet & Diana Dorobantu & Yahia Salhi, 2019. "A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 423-448, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-017-9611-2
    DOI: 10.1007/s11009-017-9611-2
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    References listed on IDEAS

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    Cited by:

    1. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    2. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.
    3. 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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