IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01258645.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01258645/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s11009-017-9611-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.
    2. Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
    3. Marceau, Etienne & Gaillardetz, Patrice, 1999. "On life insurance reserves in a stochastic mortality and interest rates environment," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 261-280, December.
    4. repec:dau:papers:123456789/9697 is not listed on IDEAS
    5. Samuel Cox & Yijia Lin, 2007. "Natural Hedging of Life and Annuity Mortality Risks," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 1-15.
    6. Delong, Å ukasz, 2012. "No-Good-Deal, Local Mean-Variance and Ambiguity Risk Pricing and Hedging for an Insurance Payment Process," ASTIN Bulletin, Cambridge University Press, vol. 42(1), pages 203-232, May.
    7. Etienne Chevalier & Thomas Lim & Ricardo Romo Roméro, 2014. "Indifference fee rate for variable annuities," Working Papers hal-01017157, HAL.
    8. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    9. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    10. Bayraktar, Erhan & Milevsky, Moshe A. & David Promislow, S. & Young, Virginia R., 2009. "Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 676-691, March.
    11. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2013. "Density approach in modelling multi-defaults," Working Papers hal-00870492, HAL.
    12. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Christophette Blanchet-Scalliet & Diana Dorobantu & Yahia Salhi, 2016. "A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives," Working Papers hal-01258645, HAL.
    3. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    4. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    5. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    6. Bensusan, Harry & El Karoui, Nicole & Loisel, Stéphane & Salhi, Yahia, 2016. "Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 61-72.
    7. Debonneuil, Edouard & Loisel, Stéphane & Planchet, Frédéric, 2018. "Do actuaries believe in longevity deceleration?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 325-338.
    8. Wang, Ting & Young, Virginia R., 2016. "Hedging pure endowments with mortality derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 238-255.
    9. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2018. "Indifference pricing of pure endowments via BSDEs under partial information," Papers 1804.00223, arXiv.org, revised Jul 2020.
    10. Francesco Menoncin & Luca Regis, 2015. "Longevity assets and pre-retirement consumption/portfolio decisions," Working Papers 2/2015, IMT School for Advanced Studies Lucca, revised May 2015.
    11. Zhou, Hongjuan & Zhou, Kenneth Q. & Li, Xianping, 2022. "Stochastic mortality dynamics driven by mixed fractional Brownian motion," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 218-238.
    12. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    13. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    14. Karim Barigou & Stéphane Loisel & Yahia Salhi, 2020. "Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect," Risks, MDPI, vol. 9(1), pages 1-18, December.
    15. Johnny Siu‐Hang Li & Andrew Cheuk‐Yin Ng, 2011. "Canonical Valuation of Mortality‐Linked Securities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(4), pages 853-884, December.
    16. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    17. Virginia R. Young, 2007. "Pricing Life Insurance under Stochastic Mortality via the Instantaneous Sharpe Ratio: Theorems and Proofs," Papers 0705.1297, arXiv.org.
    18. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    19. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
    20. Wang, Chou-Wen & Huang, Hong-Chih & Hong, De-Chuan, 2013. "A feasible natural hedging strategy for insurance companies," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 532-541.

    More about this item

    Keywords

    representative contract; life insurance; utility maximization; indifference pricing;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01258645. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.