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Loss-Aversion with Kinked Linear Utility Functions

Author

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  • Michael Best
  • Robert Grauer
  • Jaroslava Hlouskova
  • Xili Zhang

Abstract

Prospect theory postulates that the utility function is characterized by a kink (a point of non-differentiability) that distinguishes gains from losses. In this paper we present an algorithm that efficiently solves the linear version of the kinked-utility problem. First, we transform the non-differentiable kinked linear-utility problem into a higher dimensional, differentiable, linear program. Second, we introduce an efficient algorithm that solves the higher dimensional linear program in a smaller dimensional space. Third, we employ a numerical example to show that solving the problem with our algorithm is 15 times faster than solving the higher dimensional linear program using the interior point method of Mosek. Finally, we provide a direct link between the piece-wise linear programming problem and conditional value-at-risk, a downside risk measure. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:44:y:2014:i:1:p:45-65
    DOI: 10.1007/s10614-013-9391-x
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    References listed on IDEAS

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    2. Adriano Zanin Zambom & Julian A. A. Collazos & Ronaldo Dias, 2019. "Functional data clustering via hypothesis testing k-means," Computational Statistics, Springer, vol. 34(2), pages 527-549, June.
    3. Grauer, Robert R., 2013. "Limiting losses may be injurious to your wealth," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5088-5100.
    4. Michael J. Best & Robert R. Grauer, 2017. "Humans, Econs and Portfolio Choice," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-30, June.
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    7. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.

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