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: 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

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 2, 423-448

Abstract: 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.

Keywords: Indifference pricing; Representative contract; Utility maximization; Life insurance; G11; G13; G22 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-017-9611-2

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