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Discrete-Time Financial Planning Models Under Loss-Averse Preferences

Author

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  • 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
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. 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.
    4. Fortin, Ines & Hlouskova, Jaroslava, 2024. "Prospect theory and asset allocation," The Quarterly Review of Economics and Finance, Elsevier, vol. 94(C), pages 214-240.
    5. 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.
    6. 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.
    7. 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.
    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.

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