IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v53y2005i3p403-414.html
   My bibliography  Save this article

Discrete-Time Financial Planning Models Under Loss-Averse Preferences

Author

Listed:
  • Arjen Siegmann

    (Department of Finance, Vrije Universiteit Amsterdam, De Boelelaan 1105, NL, Amsterdam, The Netherlands, and Research Department, Netherlands Central Bank (DNB))

  • André Lucas

    (Department of Finance, Vrije Universiteit Amsterdam, De Boelelaan 1105, NL, Amsterdam, The Netherlands, and Tinbergen Institute, Amsterdam, The Netherlands)

Abstract

We consider a dynamic asset allocation problem formulated as a mean-shortfall model in discrete time. A characterization of the solution is derived analytically under general distributional assumptions for serially independent risky returns. The solution displays risk taking under shortfall, as well as a specific form of time diversification. Also, for a representative stock-return distribution, risk taking increases monotonically with the number of decision moments given a fixed horizon. This is related to the well-known casino effect arising in a downside-risk and expected return framework. As a robustness check, we provide results for a modified objective with a quadratic penalty on shortfall. An analytical solution for a single-stage setup is derived, and numerical results for the two-period model and time diversification are provided.

Suggested Citation

  • Arjen Siegmann & André Lucas, 2005. "Discrete-Time Financial Planning Models Under Loss-Averse Preferences," Operations Research, INFORMS, vol. 53(3), pages 403-414, June.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:3:p:403-414
    DOI: 10.1287/opre.1040.0182
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1040.0182
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1040.0182?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
    ---><---

    References listed on IDEAS

    as
    1. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    2. 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.
    3. 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..
    4. Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
    5. 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.
    6. David R. Cariño & Terry Kent & David H. Myers & Celine Stacy & Mike Sylvanus & Andrew L. Turner & Kouji Watanabe & William T. Ziemba, 1994. "The Russell-Yasuda Kasai Model: An Asset/Liability Model for a Japanese Insurance Company Using Multistage Stochastic Programming," Interfaces, INFORMS, vol. 24(1), pages 29-49, February.
    7. G. Consigli & M. Dempster, 1998. "Dynamic stochastic programmingfor asset-liability management," Annals of Operations Research, Springer, vol. 81(0), pages 131-162, June.
    8. Randall S. Hiller & Jonathan Eckstein, 1993. "Stochastic Dedication: Designing Fixed Income Portfolios Using Massively Parallel Benders Decomposition," Management Science, INFORMS, vol. 39(11), pages 1422-1438, November.
    9. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    10. 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.
    11. Cees Dert & Bart Oldenkamp, 2000. "Optimal Guaranteed Return Portfolios and the Casino Effect," Operations Research, INFORMS, vol. 48(5), pages 768-775, October.
    12. Berkelaar, A.B. & Kouwenberg, R.R.P., 2000. "Dynamic asset allocation and downside-risk aversion," Econometric Institute Research Papers EI 2000-12/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Arjan Berkelaar & Cees Dert & Bart Oldenkamp & Shuzhong Zhang, 2002. "A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming," Operations Research, INFORMS, vol. 50(5), pages 904-915, October.
    14. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    15. Zhang, S., 2002. "An interior-point and decomposition approach to multiple stage stochastic programming," Econometric Institute Research Papers EI 2002-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    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. E. Borgonovo & L. Peccati, 2010. "Moment calculations for piecewise-defined functions: an application to stochastic optimization with coherent risk measures," Annals of Operations Research, Springer, vol. 176(1), pages 235-258, April.
    2. Liu, Shuangzhe & Ma, Tiefeng & Polasek, Wolfgang, 2014. "Spatial system estimators for panel models: A sensitivity and simulation study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 78-102.
    3. 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.
    4. Michael Best & Robert Grauer & Jaroslava Hlouskova & Xili Zhang, 2014. "Loss-Aversion with Kinked Linear Utility Functions," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 45-65, June.
    5. Dormidontova, Yulia & Nazarov, Vladimir & A. Tikhonova, 2014. "Analysis of Approaches of Participants of Pension Products Market to the Development of Optimal Investment Strategies of Pension Savings," Published Papers r90227, Russian Presidential Academy of National Economy and Public Administration.
    6. André Lucas & Arjen Siegmann, 2008. "The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(1‐2), pages 200-226, January.
    7. Fortin, Ines & Hlouskova, Jaroslava, 2024. "Prospect theory and asset allocation," The Quarterly Review of Economics and Finance, Elsevier, vol. 94(C), pages 214-240.
    8. Ines Fortin & Jaroslava Hlouskova, 2015. "Downside loss aversion: Winner or loser?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 181-233, April.
    9. Shushang Zhu & Duan Li & Shouyang Wang, 2009. "Robust portfolio selection under downside risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 869-885.
    10. Fortin, Ines & Hlouskova, Jaroslava, 2012. "Optimal Asset Allocation under Quadratic Loss Aversion," Economics Series 291, Institute for Advanced Studies.

    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. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    2. Veld, Chris & Veld-Merkoulova, Yulia V., 2008. "The risk perceptions of individual investors," Journal of Economic Psychology, Elsevier, vol. 29(2), pages 226-252, April.
    3. Servaas van Bilsen & Roger J. A. Laeven & Theo E. Nijman, 2020. "Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level," Management Science, INFORMS, vol. 66(9), pages 3927-3955, September.
    4. 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.
    5. Curatola, Giuliano, 2017. "Optimal portfolio choice with loss aversion over consumption," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 345-358.
    6. 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).
    7. 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.
    8. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    9. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
    10. Yacine AÏT‐SAHALI & Michael W. Brandt, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, August.
    11. Wu, Yahao & Wang, Xiao-Tian & Wu, Min, 2009. "Fractional-moment CAPM with loss aversion," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1406-1414.
    12. Berkelaar, Arjan & Kouwenberg, Roy, 2009. "From boom 'til bust: How loss aversion affects asset prices," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1005-1013, June.
    13. Azzato, Jeffrey & Krawczyk, Jacek B & Sissons, Christopher, 2011. "On loss-avoiding lump-sum pension optimization with contingent targets," Working Paper Series 18552, Victoria University of Wellington, School of Economics and Finance.
    14. Curatola, Giuliano, 2016. "Optimal consumption and portfolio choice with loss aversion," SAFE Working Paper Series 130, Leibniz Institute for Financial Research SAFE.
    15. Armstrong, John & Brigo, Damiano, 2019. "Risk managing tail-risk seekers: VaR and expected shortfall vs S-shaped utility," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 122-135.
    16. 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.
    17. Huy N. Chau & Mikl'os R'asonyi, 2016. "Skorohod's representation theorem and optimal strategies for markets with frictions," Papers 1606.07311, arXiv.org, revised Apr 2017.
    18. 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.
    19. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    20. Azzato, Jeffrey & Krawczyk, Jacek B & Sissons, Christopher, 2011. "On loss-avoiding lump-sum pension optimization with contingent targets," Working Paper Series 1532, Victoria University of Wellington, School of Economics and Finance.

    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:inm:oropre:v:53:y:2005:i:3:p:403-414. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.