IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v147y2021ics096007792100271x.html
   My bibliography  Save this article

Portfolio optimization under safety first expected utility with nonlinear probability distortion

Author

Listed:
  • Li, Yan
  • Mi, Hui

Abstract

In this paper, we study a portfolio selection problem under safety first expected utility model with distortion (SFEUD model) where the underlying probability scale is transformed by a nonlinear distortion function. By employing the quantile formulation and the relaxation method, we obtain the general form of optimal solution to the problem, and the necessary and sufficient condition for existing such an optimal solution is also proved. We further demonstrate an analytical solution to the optimal strategies under four different monotonic cases. What’s more, the optimal terminal wealth process is replicated into a portfolio of options and deposits under specific circumstances. In addition, we empirically verify the model implication and figure out that investors’ realization of disaster risk can explain the price change of call options to some degree.

Suggested Citation

  • Li, Yan & Mi, Hui, 2021. "Portfolio optimization under safety first expected utility with nonlinear probability distortion," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s096007792100271x
    DOI: 10.1016/j.chaos.2021.110917
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792100271X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110917?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. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
    2. 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.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. 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.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    8. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    9. Hanqing Jin & Jianming Xia & Xun Yu Zhou, 2019. "Arrow–Debreu equilibria for rank‐dependent utilities with heterogeneous probability weighting," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 898-927, July.
    10. M. C. Chiu & D. Li, 2009. "Asset-Liability Management Under the Safety-First Principle," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 455-478, December.
    11. Bi, Junna & Jin, Hanqing & Meng, Qingbin, 2018. "Behavioral mean-variance portfolio selection," European Journal of Operational Research, Elsevier, vol. 271(2), pages 644-663.
    12. Levy, Haim & Levy, Moshe, 2009. "The safety first expected utility model: Experimental evidence and economic implications," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1494-1506, August.
    13. Zuo Quan Xu & Xun Yu Zhou & Sheng Chao Zhuang, 2019. "Optimal insurance under rank‐dependent utility and incentive compatibility," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 659-692, April.
    14. Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2018. "Dynamic safety first expected utility model," European Journal of Operational Research, Elsevier, vol. 271(1), pages 141-154.
    15. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
    Full references (including those not matched with items on IDEAS)

    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. Zuo Quan Xu, 2021. "Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory," Papers 2108.06940, arXiv.org, revised Aug 2022.
    2. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    3. Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2018. "Dynamic safety first expected utility model," European Journal of Operational Research, Elsevier, vol. 271(1), pages 141-154.
    4. Bi, Xiuchun & Cui, Zhenyu & Fan, Jiacheng & Yuan, Lvning & Zhang, Shuguang, 2023. "Optimal investment problem under behavioral setting: A Lagrange duality perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    5. Zuo Quan Xu, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    6. Xu Zuo Quan & Zhou Xun Yu & Zhuang Sheng Chao, 2015. "Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities," Papers 1509.04839, arXiv.org.
    7. 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.
    8. Boonen, Tim J. & Jiang, Wenjun, 2022. "Bilateral risk sharing in a comonotone market with rank-dependent utilities," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 361-378.
    9. Weiping Wu & Yu Lin & Jianjun Gao & Ke Zhou, 2023. "Mean-variance hybrid portfolio optimization with quantile-based risk measure," Papers 2303.15830, arXiv.org, revised Apr 2023.
    10. Rania HENTATI & Jean-Luc PRIGENT, 2010. "Structured Portfolio Analysis under SharpeOmega Ratio," EcoMod2010 259600073, EcoMod.
    11. Stephen G Dimmock & Roy Kouwenberg & Olivia S Mitchell & Kim Peijnenburg, 2021. "Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field," The Review of Financial Studies, Society for Financial Studies, vol. 34(9), pages 4524-4563.
    12. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    13. 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.
    14. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    15. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2020. "Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time," Papers 2006.01979, arXiv.org.
    16. Yam, Sheung Chi Phillip & Yang, Hailiang & Yuen, Fei Lung, 2016. "Optimal asset allocation: Risk and information uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 554-561.
    17. Liurui Deng & Traian A. Pirvu, 2016. "Multi-period investment strategies under Cumulative Prospect Theory," Papers 1608.08490, arXiv.org, revised Mar 2019.
    18. Li, Yongwu & Xu, Zuo Quan, 2017. "Optimal insurance design with a bonus," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 111-118.
    19. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2020. "Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time," Working Papers hal-02624308, HAL.
    20. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2023. "Optimal moral-hazard-free reinsurance under extended distortion premium principles," Papers 2304.08819, arXiv.org.

    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:chsofr:v:147:y:2021:i:c:s096007792100271x. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.