IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v88y2019icp93-107.html
   My bibliography  Save this article

Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences

Author

Listed:
  • Chong, Wing Fung

Abstract

By applying the principle of equivalent forward preferences, this paper revisits the pricing and hedging problems for equity-linked life insurance contracts. The equity-linked contingent claim depends on, not only the future lifetime of the policyholder, but also the performance of the reference portfolio in the financial market for the segregated account of the policyholder. For both zero volatility and non-zero volatility forward utility preferences, prices and hedging strategies of the contract are represented by solutions of random horizon backward stochastic differential equations. Numerical illustration is provided for the zero volatility case. The derived prices and hedging strategies are also compared with classical results in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:88:y:2019:i:c:p:93-107
    DOI: 10.1016/j.insmatheco.2019.06.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668718303998
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2019.06.003?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. Virginia R. Young, 2004. "Pricing In An Incomplete Market With An Affine Term Structure," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 359-381, July.
    2. Traian A. Pirvu & Huayue Zhang, 2013. "Utility Indifference Pricing: A Time Consistent Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 304-326, September.
    3. 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.
    4. Sergey Nadtochiy & Thaleia Zariphopoulou, 2018. "Optimal contract for a fund manager, with capital injections and endogenous trading constraints," Papers 1802.09165, arXiv.org.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. (*), Thaleia Zariphopoulou & George M. Constantinides, 1999. "Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences," Finance and Stochastics, Springer, vol. 3(3), pages 345-369.
    7. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    8. George M. Constantinides & Thaleia Zariphopoulou, 2001. "Bounds on Derivative Prices in an Intertemporal Setting with Proportional Transaction Costs and Multiple Securities," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 331-346, July.
    9. repec:dau:papers:123456789/9697 is not listed on IDEAS
    10. Łukasz Delong, 2019. "Optimal investment for insurance company with exponential utility and wealth-dependent risk aversion coefficient," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 73-113, February.
    11. Bahman Angoshtari & Thaleia Zariphopoulou & Xun Yu Zhou, 2016. "Predictable Forward Performance Processes: The Binomial Case," Papers 1611.04494, arXiv.org, revised Mar 2019.
    12. 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.
    13. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    14. Wing Fung Chong & Gechun Liang, 2018. "Optimal investment and consumption with forward preferences and uncertain parameters," Papers 1807.01186, arXiv.org, revised Nov 2023.
    15. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    16. 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.
    17. Föllmer, H. & Schweizer, M., 1988. "Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 147-160, November.
    18. 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.
    19. 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.
    20. Levon Avanesyan & Mykhaylo Shkolnikov & Ronnie Sircar, 2018. "Construction of Forward Performance Processes in Stochastic Factor Models and an Extension of Widder's Theorem," Papers 1805.04535, arXiv.org.
    21. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.
    22. Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior," Finance and Stochastics, Springer, vol. 23(1), pages 239-273, January.
    23. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    24. Brennan, Michael J & Schwartz, Eduardo S, 1979. "Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance Policies with an Asset Value Guarantee," The Journal of Business, University of Chicago Press, vol. 52(1), pages 63-93, January.
    25. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    26. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    27. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
    28. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    29. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    30. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    31. Borch, Karl, 1963. "Recent Developments in Economic Theory and their Application to Insurance," ASTIN Bulletin, Cambridge University Press, vol. 2(3), pages 322-341, April.
    32. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    33. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    34. Sergey Nadtochiy & Michael Tehranchi, 2017. "Optimal Investment For All Time Horizons And Martin Boundary Of Space-Time Diffusions," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 438-470, April.
    35. M. Musiela & T. Zariphopoulou, 2011. "Initial Investment Choice And Optimal Future Allocations Under Time-Monotone Performance Criteria," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 61-81.
    36. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, 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. Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2021. "Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    2. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    3. Gechun Liang & Yifan Sun & Thaleia Zariphopoulou, 2023. "Representation of forward performance criteria with random endowment via FBSDE and application to forward optimized certainty equivalent," Papers 2401.00103, arXiv.org.
    4. Gechun Liang & Moris S. Strub & Yuwei Wang, 2023. "Predictable Relative Forward Performance Processes: Multi-Agent and Mean Field Games for Portfolio Management," Papers 2311.04841, arXiv.org, revised Dec 2023.
    5. Ye, Jinchun, 2019. "Stochastic utilities with subsistence and satiation: Optimal life insurance purchase, consumption and investment," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 193-212.
    6. Gechun Liang & Moris S. Strub & Yuwei Wang, 2021. "Predictable Forward Performance Processes: Infrequent Evaluation and Applications to Human-Machine Interactions," Papers 2110.08900, arXiv.org, revised Dec 2023.
    7. Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2021. "Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences," Papers 2106.13888, arXiv.org.
    8. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    9. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2021. "Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 683-721, April.

    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. 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.
    2. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, 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. Wing Fung Chong & Gechun Liang, 2018. "Optimal investment and consumption with forward preferences and uncertain parameters," Papers 1807.01186, arXiv.org, revised Nov 2023.
    5. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2019. "Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion," Papers 1904.01745, arXiv.org.
    7. Virginia R. Young, 2004. "Pricing In An Incomplete Market With An Affine Term Structure," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 359-381, July.
    8. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2021. "Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 683-721, April.
    9. 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.
    10. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    11. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    12. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    13. repec:dau:papers:123456789/5374 is not listed on IDEAS
    14. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    15. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    16. repec:abd:kauiea:v:30:y:2017:i:2:p:135-157 is not listed on IDEAS
    17. Alexander Melnikov & Yuliya Romanyuk, 2008. "Efficient Hedging And Pricing Of Equity-Linked Life Insurance Contracts On Several Risky Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 295-323.
    18. Jumadil Saputra & Suhal Kusairi & Nur Azura Sanusi, 2017. "Modeling the Premium and Contract Properties of Family Takaful (Islamic Life Insurance) نمذجة قسط وخصائص عقد التكافل الأسري (التأمين الإسلامي على الحياة)," Journal of King Abdulaziz University: Islamic Economics, King Abdulaziz University, Islamic Economics Institute., vol. 30(2), pages 135-157, July.
    19. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    20. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    21. Jensen, Bjarne Astrup & Sørensen, Carsten, 2000. "Paying for minimum interest rate guarantees: Who should compensate who?," Working Papers 2000-1, Copenhagen Business School, Department of Finance.
    22. Mahayni, Antje & Schlögl, Erik, 2003. "The Risk Management of Minimum Return Guarantees," Bonn Econ Discussion Papers 18/2003, University of Bonn, Bonn Graduate School of Economics (BGSE).

    More about this item

    Keywords

    Equity-linked life insurance; Pricing and hedging; Indifference approach; Forward utility preferences; Random horizon BSDEs;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:eee:insuma:v:88:y:2019:i:c:p:93-107. 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.