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Constrained non-concave utility maximization: An application to life insurance contracts with guarantees

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  • Chen, An
  • Hieber, Peter
  • Nguyen, Thai

Abstract

We study a problem of non-concave utility maximization under a fair pricing constraint. The framework finds many applications in, for example, the optimal design of managerial compensation or equity-linked life insurance contracts. Deriving closed-form solutions, we observe that the fair pricing constraint will reduce the riskiness of the optimal strategies substantially. In an extensive numerical section, we analyze innovative retirement products that adapt the investment strategy of the premium pool according to the policyholder’s preferences, modeled as constant relative risk aversion (CRRA). Such products are a response to the loss of attractiveness of traditional life insurance contracts with guarantees that are negatively affected by increasing solvency requirements for return guarantees and a general decrease in interest rate levels. Taking into account that retirement products are usually tax-privileged, we find that fairly priced guarantee contracts that follow this optimal investment strategy lead to a higher expected utility level than asset investments.

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  • Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:3:p:1119-1135
    DOI: 10.1016/j.ejor.2018.09.002
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    as
    1. Lin, Hongcan & Saunders, David & Weng, Chengguo, 2017. "Optimal investment strategies for participating contracts," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 137-155.
    2. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    3. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    4. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    5. Døskeland, Trond M. & Nordahl, Helge A., 2008. "Optimal pension insurance design," Journal of Banking & Finance, Elsevier, vol. 32(3), pages 382-392, March.
    6. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    7. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    8. Antje Mahayni & Judith C. Schneider, 2016. "Minimum return guarantees, investment caps, and investment flexibility," Review of Derivatives Research, Springer, vol. 19(2), pages 85-111, July.
    9. Kasper Larsen, 2005. "Optimal portfolio delegation when parties have different coefficients of risk aversion," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 503-512.
    10. Huang, Huaxiong & Milevsky, Moshe A., 2016. "Longevity risk and retirement income tax efficiency: A location spending rate puzzle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 50-62.
    11. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    12. Davies, James B, 1981. "Uncertain Lifetime, Consumption, and Dissaving in Retirement," Journal of Political Economy, University of Chicago Press, vol. 89(3), pages 561-577, June.
    13. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    14. Carole Bernard & Xuedong He & Jia-An Yan & Xun Yu Zhou, 2015. "Optimal Insurance Design Under Rank-Dependent Expected Utility," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 154-186, January.
    15. Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
    16. Suleyman Basak & Anna Pavlova & Alexander Shapiro, 2007. "Optimal Asset Allocation and Risk Shifting in Money Management," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1583-1621, 2007 21.
    17. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
    18. Marco Nicolosi & Flavio Angelini & Stefano Herzel, 2018. "Portfolio management with benchmark related incentives under mean reverting processes," Annals of Operations Research, Springer, vol. 266(1), pages 373-394, July.
    19. 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.
    20. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 25-61, August.
    21. Bohnert, Alexander & Born, Patricia & Gatzert, Nadine, 2014. "Dynamic hybrid products in life insurance: Assessing the policyholders’ viewpoint," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 87-99.
    22. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    23. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    24. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    25. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    26. 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.
    27. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
    28. Mahayni, Antje & Schneider, Judith C., 2012. "Variable annuities and the option to seek risk: Why should you diversify?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2417-2428.
    29. Alain Bensoussan & Abel Cadenillas & Hyeng Keun Koo, 2015. "Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 902-914, October.
    30. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    31. Stephen A. Ross, 2004. "Compensation, Incentives, and the Duality of Risk Aversion and Riskiness," Journal of Finance, American Finance Association, vol. 59(1), pages 207-225, February.
    32. Robert B. Barsky & F. Thomas Juster & Miles S. Kimball & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 537-579.
    33. Pierre‐André Chiappori & Monica Paiella, 2011. "Relative Risk Aversion Is Constant: Evidence From Panel Data," Journal of the European Economic Association, European Economic Association, vol. 9(6), pages 1021-1052, December.
    34. Dietmar P.J. Leisen, 2015. "Dynamic risk taking with bonus schemes," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1583-1596, September.
    35. 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.
    36. El Karoui, Nicole & Jeanblanc, Monique & Lacoste, Vincent, 2005. "Optimal portfolio management with American capital guarantee," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 449-468, March.
    37. Hato Schmeiser & Joël Wagner, 2015. "A Proposal on How the Regulator Should Set Minimum Interest Rate Guarantees in Participating Life Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(3), pages 659-686, September.
    38. Busra Zeynep Temocin & Ralf Korn & A. Sevtap Selcuk-Kestel, 2018. "Constant proportion portfolio insurance in defined contribution pension plan management under discrete-time trading," Annals of Operations Research, Springer, vol. 260(1), pages 515-544, January.
    39. Maxim Bichuch & Stephan Sturm, 2014. "Portfolio optimization under convex incentive schemes," Finance and Stochastics, Springer, vol. 18(4), pages 873-915, October.
    40. Pézier, Jacques & Scheller, Johanna, 2013. "Best portfolio insurance for long-term investment strategies in realistic conditions," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 263-274.
    41. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.
    42. Sundaresan, Suresh & Zapatero, Fernando, 1997. "Valuation, Optimal Asset Allocation and Retirement Incentives of Pension Plans," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 631-660.
    43. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, January.
    44. Damir Filipović & Robert Kremslehner & Alexander Muermann, 2015. "Optimal Investment and Premium Policies Under Risk Shifting and Solvency Regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(2), pages 261-288, June.
    45. Chen, An & Hieber, Peter, 2016. "Optimal Asset Allocation In Life Insurance: The Impact Of Regulation," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 605-626, September.
    46. Holger Kraft & Claus Munk, 2011. "Optimal Housing, Consumption, and Investment Decisions over the Life Cycle," Management Science, INFORMS, vol. 57(6), pages 1025-1041, June.
    47. Nadine Gatzert & Carin Huber & Hato Schmeiser, 2011. "On the Valuation of Investment Guarantees in Unit-linked Life Insurance: A Customer Perspective," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(1), pages 3-29, January.
    48. Busra Zeynep Temocin & Ralf Korn & A. Sevtap Selcuk-Kestel, 2018. "Constant proportion portfolio insurance in defined contribution pension plan management," Annals of Operations Research, Springer, vol. 266(1), pages 329-348, July.
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    3. An Chen & Mitja Stadje & Fangyuan Zhang, 2020. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Papers 2002.02229, arXiv.org, revised Jun 2022.
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    5. Jennifer Alonso Garcia & Michael Sherris & Samuel Thirurajah & Jonathan Ziveyi, 2020. "Taxation and policyholder behavior: the case of guaranteed minimum accumulation benefits," ULB Institutional Repository 2013/307889, ULB -- Universite Libre de Bruxelles.
    6. Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2021. "Indifference pricing of insurance-linked securities in a multi-period model," European Journal of Operational Research, Elsevier, vol. 289(2), pages 793-805.
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    10. Hieber, Peter & Lucas, Nathalie, 2020. "Life-Care Tontines," LIDAM Discussion Papers ISBA 2020026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Antje Mahayni & Oliver Lubos & Sascha Offermann, 2021. "Minimum return rate guarantees under default risk: optimal design of quantile guarantees," Review of Managerial Science, Springer, vol. 15(7), pages 1821-1848, October.
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    14. Hanna, Vanessa & Hieber, Peter & Devolder, Pierre, 2021. "Mixed participating and unit-linked life insurance contracts: design, pricing and optimal strategy," LIDAM Discussion Papers ISBA 2021010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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