IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2403.16228.html
   My bibliography  Save this paper

Rank-Dependent Predictable Forward Performance Processes

Author

Listed:
  • Bahman Angoshtari
  • Shida Duan

Abstract

Predictable forward performance processes (PFPPs) are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead. This is a common scenario in which a controlling agent frequently re-calibrates her model. We introduce a new class of PFPPs based on rank-dependent utility, generalizing existing models that are based on expected utility theory (EUT). We establish existence of rank-dependent PFPPs under a conditionally complete market and exogenous probability distortion functions which are updated periodically. We show that their construction reduces to solving an integral equation that generalizes the integral equation obtained under EUT in previous studies. We then propose a new approach for solving the integral equation via theory of Volterra equations. We illustrate our result in the special case of conditionally complete Black-Scholes model.

Suggested Citation

  • Bahman Angoshtari & Shida Duan, 2024. "Rank-Dependent Predictable Forward Performance Processes," Papers 2403.16228, arXiv.org.
    • Handle: RePEc:arx:papers:2403.16228
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2403.16228
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Jianming Xia & Xun Yu Zhou, 2016. "Arrow–Debreu Equilibria For Rank-Dependent Utilities," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 558-588, July.
    3. 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.
    4. repec:dau:papers:123456789/2317 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Zuo Quan Xu, 2013. "A New Characterization of Comonotonicity and its Application in Behavioral Finance," Papers 1311.6080, arXiv.org, revised Jun 2014.
    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, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    2. Jing Peng & Pengyu Wei & Zuo Quan Xu, 2022. "Relative growth rate optimization under behavioral criterion," Papers 2211.05402, arXiv.org.
    3. 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.
    4. Shi, Yun & Cui, Xiangyu & Zhou, Xunyu, 2020. "Beta and Coskewness Pricing: Perspective from Probability Weighting," SocArXiv 5rqhv, Center for Open Science.
    5. 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.
    6. Zuo Quan Xu, 2014. "A Note on the Quantile Formulation," Papers 1403.7269, arXiv.org, revised Apr 2014.
    7. Guo, Jing & He, Xue Dong, 2017. "Equilibrium asset pricing with Epstein-Zin and loss-averse investors," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 86-108.
    8. 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.
    9. Xiangyu Wang & Jianming Xia & Zuo Quan Xu & Zhou Yang, 2020. "Minimal Quantile Functions Subject to Stochastic Dominance Constraints," Papers 2008.02420, arXiv.org, revised Aug 2022.
    10. Li, Yan & Mi, Hui, 2021. "Portfolio optimization under safety first expected utility with nonlinear probability distortion," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    11. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximization with intractable claims," Papers 2304.06938, arXiv.org, revised Jul 2023.
    12. van Bilsen, Servaas & Laeven, Roger J.A., 2020. "Dynamic consumption and portfolio choice under prospect theory," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 224-237.
    13. 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.
    14. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    15. 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.
    16. Xue Dong He & Zhaoli Jiang, 2020. "Optimal Payoff under the Generalized Dual Theory of Choice," Papers 2012.00345, arXiv.org.
    17. Johannes G. Jaspersen & Richard Peter & Marc A. Ragin, 2023. "Probability weighting and insurance demand in a unified framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 63-109, March.
    18. 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.
    19. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Wang, 2002. "Consistent testing for stochastic dominance: a subsampling approach," CeMMAP working papers 03/02, Institute for Fiscal Studies.
    20. van den Bergh, J.C.J.M. & Botzen, W.J.W., 2015. "Monetary valuation of the social cost of CO2 emissions: A critical survey," Ecological Economics, Elsevier, vol. 114(C), pages 33-46.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2403.16228. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.