IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v77y2017icp119-132.html
   My bibliography  Save this article

Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process

Author

Listed:
  • Liang, Xiaoqing
  • Lu, Yi

Abstract

In this paper, we investigate the pricing problem for a portfolio of life insurance contracts where the life contingent payments are equity-linked depending on the performance of a risky stock or index. The shot-noise effects are incorporated in the modeling of stock prices, implying that sudden jumps in the stock price are allowed, but their effects may gradually decline over time. The contracts are priced using the principle of equivalent utility. Under the assumption of exponential utility, we find the optimal investment strategy and show that the indifference premium solves a non-linear partial integro-differential equation (PIDE). The Feynman–Kač form solutions are derived for two special cases of the PIDE. We further discuss the problem for the asymptotic shot-noise process, and find the probabilistic representation of the indifference premium. We also provide some numerical examples and analyze parameter sensitivities for the results obtained in this paper.

Suggested Citation

  • Liang, Xiaoqing & Lu, Yi, 2017. "Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 119-132.
    • Handle: RePEc:eee:insuma:v:77:y:2017:i:c:p:119-132
    DOI: 10.1016/j.insmatheco.2017.09.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668716304139
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2017.09.002?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Junna Bi & Junyi Guo, 2010. "Hedging unit‐linked life insurance contracts in a financial market driven by shot‐noise processes," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(5), pages 609-623, September.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Jaimungal, Sebastian & Young, Virginia R., 2005. "Pricing equity-linked pure endowments with risky assets that follow Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 329-346, June.
    5. Virginia Young, 2003. "Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equivalent Utility," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 68-86.
    6. Moore, Kristen S. & Young, Virginia R., 2003. "Pricing equity-linked pure endowments via the principle of equivalent utility," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 497-516, December.
    7. Timo Altmann & Thorsten Schmidt & Winfried Stute, 2008. "A Shot Noise Model For Financial Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 87-106.
    8. Schmidt, Thorsten & Stute, Winfried, 2007. "Shot-noise processes and the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1332-1338, July.
    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. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Post-Print hal-02896141, HAL.
    2. Karim Barigou & Lukasz Delong, 2020. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Papers 2007.08804, arXiv.org, revised Nov 2021.
    3. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    4. Yiqing Chen, 2019. "A Renewal Shot Noise Process with Subexponential Shot Marks," Risks, MDPI, vol. 7(2), pages 1-8, June.
    5. Alessandra Cretarola & Benedetta Salterini, 2023. "Utility-based indifference pricing of pure endowments in a Markov-modulated market model," Papers 2301.13575, arXiv.org.
    6. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Working Papers hal-02896141, HAL.
    7. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    8. Fan He & Xuansen He, 2019. "A Continuous Differentiable Wavelet Shrinkage Function for Economic Data Denoising," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 729-761, August.
    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.

    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. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    2. Alessandra Cretarola & Benedetta Salterini, 2023. "Utility-based indifference pricing of pure endowments in a Markov-modulated market model," Papers 2301.13575, arXiv.org.
    3. Jaimungal, Sebastian & Young, Virginia R., 2005. "Pricing equity-linked pure endowments with risky assets that follow Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 329-346, June.
    4. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    7. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    8. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
    9. Shuang Li & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2017. "Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 276-295, May.
    10. Ma, Jin & Yun, Youngyun, 2010. "Correlated intensity, counter party risks, and dependent mortalities," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 337-351, December.
    11. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    12. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    13. Patrick Brockett & Linda Goldens & Min-Ming Wen & Charles Yang, 2009. "Pricing Weather Derivatives Using the Indifference Pricing Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 303-315.
    14. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    15. 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.
    16. Fu, Jun & Yang, Hailiang, 2012. "Equilibruim approach of asset pricing under Lévy process," European Journal of Operational Research, Elsevier, vol. 223(3), pages 701-708.
    17. Kai Kopperschmidt & Winfried Stute, 2009. "Purchase timing models in marketing: a review," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(2), pages 123-149, June.
    18. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    19. Antje Mahayni & Matthias Muck, 2017. "The benefit of life insurance contracts with capped index participation when stock prices are subject to jump risk," Review of Derivatives Research, Springer, vol. 20(3), pages 281-308, October.
    20. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.

    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:eee:insuma:v:77:y:2017:i:c:p:119-132. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.