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Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment

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Author Info

  • Xue Dong He

    ()
    (Industrial Engineering and Operations Research Department, Columbia University, New York, New York 10027)

  • Xun Yu Zhou

    ()
    (Nomura Centre for Mathematical Finance, University of Oxford, Oxford OX1 3LB, United Kingdom; Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford OX2 6ED, United Kingdom; and Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, Hong Kong)

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    Abstract

    We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting. This paper was accepted by Wei Xiong, finance.

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    File URL: http://dx.doi.org/10.1287/mnsc.1100.1269
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 57 (2011)
    Issue (Month): 2 (February)
    Pages: 315-331

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    Handle: RePEc:inm:ormnsc:v:57:y:2011:i:2:p:315-331

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    Keywords: portfolio choice; single period; cumulative prospect theory; reference point; loss aversion; S-shaped utility function; probability weighting; well-posedness;

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    Cited by:
    1. Hlouskova, Jaroslava & Tsigaris, Panagiotis, 2012. "Capital Income Taxation and Risk Taking under Prospect Theory," Economics Series 283, Institute for Advanced Studies.
    2. Miklos Rasonyi & Andrea M. Rodrigues, 2012. "Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets," Papers 1202.0628, arXiv.org, revised Apr 2013.
    3. Shuangzhe Liu & Tiefeng Ma & Wolfgang Polasek, 2012. "Spatial System Estimators for Panel Models: A Sensitivity and Simulation Study," Working Paper Series 75_12, The Rimini Centre for Economic Analysis.
    4. Hlouskova, Jaroslava & Tsigaris, Panagiotis, 2012. "What Does it Take for a Specific Prospect Theory Type Household to Engage in Risky Investment?," Economics Series 286, Institute for Advanced Studies.
    5. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    6. Fortin, Ines & Hlouskova, Jaroslava, 2012. "Optimal Asset Allocation under Quadratic Loss Aversion," Economics Series 291, Institute for Advanced Studies.
    7. De Giorgi, Enrico G. & Legg, Shane, 2012. "Dynamic portfolio choice and asset pricing with narrow framing and probability weighting," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 951-972.
    8. Ghossoub, Mario, 2011. "Towards a Purely Behavioral Definition of Loss Aversion," MPRA Paper 37628, University Library of Munich, Germany, revised 23 Mar 2012.
    9. Foster, Jarred & Krawczyk, Jacek B, 2013. "Sensitivity of cautious-relaxed investment policies to target variation," Working Paper Series 2972, Victoria University of Wellington, School of Economics and Finance.
    10. Matteo Del Vigna, 2011. "Financial market equilibria with heterogeneous agents: CAPM and market segmentation," Working Papers - Mathematical Economics 2011-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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