A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives
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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.
KeywordsIndifference pricing Representative contract Utility maximization Life insurance
Mathematics Subject Classification (2010)G11 G13 G22
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This work is funded by ANR Research Project “LoLitA” (ANR-13-BS01-0011). Y. Salhi’s work has been supported by the BNP Paribas Cardif Chair ”Data Analytics and Models in Insurance”. The views expressed in this document are the authors owns and do not necessarily reflect those endorsed by BNP Paribas Cardif. The authors would like to thank the anonymous referee for his/her careful reading and his/her remarks which improved the presentation of the paper.
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