IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v79y2018icp194-209.html
   My bibliography  Save this article

Optimal investment under VaR-Regulation and Minimum Insurance

Author

Listed:
  • Chen, An
  • Nguyen, Thai
  • Stadje, Mitja

Abstract

We look at an optimal investment problem of a financial institution operating under a joint Value-at-Risk and a portfolio insurance constraint. This analysis is particularly relevant for an insurance company operating under the Solvency II regulation which aims to maximize the expected utility of its shareholders, while at the same time being required to provide its policyholders a minimum guaranteed amount. Using static Lagrangian method, we solve the pointwise utility optimization problem to achieve the global maximum by carefully comparing the local maximizers with the jump point or the boundary. Our theoretical and numerical results show that contrary to a pure Value-at-Risk regulation, an insurance company that operates not only under a Solvency II VaR constraint but additionally has to serve a minimal guarantee admits a comprehensive but not too costly protection, and at the same time displays prudent investment behavior. This result holds for both constant and stochastic volatility settings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:194-209
    DOI: 10.1016/j.insmatheco.2018.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717302123
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2018.01.008?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. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
    2. Bjarne Astrup Jensen & Carsten Sørensen, 2001. "Paying for Minimum Interest Rate Guarantees: Who Should Compensate Who?," European Financial Management, European Financial Management Association, vol. 7(2), pages 183-211, June.
    3. Colin Pugh, 2006. "Funding Rules and Actuarial Methods," OECD Working Papers on Insurance and Private Pensions 1, OECD Publishing.
    4. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    5. Colin Pugh & Juan Yermo, 2008. "Funding Regulations and Risk Sharing," OECD Working Papers on Insurance and Private Pensions 17, OECD Publishing.
    6. Kaplanski, Guy & Levy, Haim, 2007. "Basel's value-at-risk capital requirement regulation: An efficiency analysis," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1887-1906, June.
    7. Grossman, Sanford J & Vila, Jean-Luc, 1989. "Portfolio Insurance in Complete Markets: A Note," The Journal of Business, University of Chicago Press, vol. 62(4), pages 473-476, October.
    8. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    9. Broeders, Dirk & Chen, An, 2010. "Pension regulation and the market value of pension liabilities: A contingent claims analysis using Parisian options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1201-1214, June.
    10. Shi, Zhen & Werker, Bas J.M., 2012. "Short-horizon regulation for long-term investors," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3227-3238.
    11. Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    12. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    13. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    16. Branger, Nicole & Schlag, Christian & Schneider, Eva, 2008. "Optimal portfolios when volatility can jump," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1087-1097, June.
    17. 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.
    18. Colin Pugh & Juan Yermo, 2008. "Funding regulations and risk sharing," OECD Journal: Financial Market Trends, OECD Publishing, vol. 2008(1), pages 163-196.
    19. Ralf Korn & Holger Kraft, 2004. "On The Stability Of Continuous‐Time Portfolio Problems With Stochastic Opportunity Set," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 403-414, July.
    20. Grossman, Sanford J & Zhou, Zhongquan, 1996. "Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
    21. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    22. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-1090.
    23. Linton, Oliver & Xiao, Zhijie, 2013. "Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 29(4), pages 771-807, August.
    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. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
    2. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
    3. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, June.
    4. Bi, Junna & Cai, Jun, 2019. "Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 1-14.
    5. Mi, Hui & Xu, Zuo Quan, 2023. "Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 82-105.
    6. Frank Bosserhoff & An Chen & Nils Sorensen & Mitja Stadje, 2021. "On the Investment Strategies in Occupational Pension Plans," Papers 2104.08956, arXiv.org.
    7. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    8. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    9. Marcos Escobar-Anel & Yevhen Havrylenko & Rudi Zagst, 2022. "Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model," Papers 2208.14152, arXiv.org, revised Oct 2023.
    10. An Chen & Thai Nguyen & Mitja Stadje, 2018. "Risk management with multiple VaR constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 297-337, October.
    11. 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.
    12. Christian Dehm & Thai Nguyen & Mitja Stadje, 2020. "Non-concave expected utility optimization with uncertain time horizon," Papers 2005.13831, arXiv.org, revised Oct 2021.
    13. Hui Mi & Zuo Quan Xu & Dongfang Yang, 2023. "Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint," Papers 2309.01936, arXiv.org.

    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. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
    2. Jang, Bong-Gyu & Park, Seyoung, 2016. "Ambiguity and optimal portfolio choice with Value-at-Risk constraint," Finance Research Letters, Elsevier, vol. 18(C), pages 158-176.
    3. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    4. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    5. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    6. Marcos Escobar-Anel & Yevhen Havrylenko & Rudi Zagst, 2022. "Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model," Papers 2208.14152, arXiv.org, revised Oct 2023.
    7. An Chen & Thai Nguyen & Mitja Stadje, 2018. "Risk management with multiple VaR constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 297-337, October.
    8. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    9. Danielsson, Jon & Shin, Hyun Song & Zigrand, Jean-Pierre, 2004. "The impact of risk regulation on price dynamics," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 1069-1087, May.
    10. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    11. Dangl, Thomas & Randl, Otto & Zechner, Josef, 2016. "Risk control in asset management: Motives and concepts," CFS Working Paper Series 546, Center for Financial Studies (CFS).
    12. M. Escobar-Anel & M. Kschonnek & R. Zagst, 2023. "Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 23(12), pages 1793-1813, November.
    13. Das, Sanjiv R. & Statman, Meir, 2013. "Options and structured products in behavioral portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 137-153.
    14. 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.
    15. Mei Choi Chiu & Hoi Ying Wong & Duan Li, 2012. "Roy’s Safety‐First Portfolio Principle in Financial Risk Management of Disastrous Events," Risk Analysis, John Wiley & Sons, vol. 32(11), pages 1856-1872, November.
    16. Basak, Suleyman, 2002. "A comparative study of portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1217-1241, July.
    17. Marcos Escobar-Anel & Harold A. Moreno-Franco, 2019. "Dynamic portfolio strategies under a fully correlated jump-diffusion process," Annals of Finance, Springer, vol. 15(3), pages 421-453, September.
    18. N. Naguez & J. L. Prigent, 2017. "Optimal portfolio positioning within generalized Johnson distributions," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1037-1055, July.
    19. Kaplanski, Guy & Levy, Haim, 2007. "Basel's value-at-risk capital requirement regulation: An efficiency analysis," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1887-1906, June.
    20. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.

    More about this item

    Keywords

    Value at Risk; Optimal portfolio; Portfolio insurance; Risk management; Solvency II regulation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

    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:79:y:2018:i:c:p:194-209. 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.