BEHAVIORAL PORTFOLIO CHOICE UNDER HYPERBOLIC ABSOLUTE RISK AVERSION

Marcos Escobar-Anel, Andreas Lichtenstern () and Rudi Zagst ()
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Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Canada
Andreas Lichtenstern: #x2020;Department of Mathematics, Technical University of Munich, Munich, Germany
Rudi Zagst: #x2020;Department of Mathematics, Technical University of Munich, Munich, Germany
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 07, 1-33

Abstract: This paper studies the optimal investment problem for a behavioral investor with probability distortion functions and an S-shaped utility function whose utility on gains satisfies the Inada condition at infinity, albeit not necessarily at zero, in a complete continuous-time financial market model. In particular, a piecewise utility function with hyperbolic absolute risk aversion (HARA) is applied. The considered behavioral framework, cumulative prospect theory (CPT), was originally introduced by [A. Tversky & D. Kahneman (1992) Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (4), 297–323]. The utility model allows for increasing, constant or decreasing relative risk aversion. The continuous-time portfolio selection problem under the S-shaped HARA utility function in combination with probability distortion functions on gains and losses is solved theoretically for the first time, the optimal terminal wealth and its replicating wealth process and investment strategy are stated. In addition, conditions on the utility and the probability distortion functions for well-posedness and closed-form solutions are provided. A specific probability distortion function family is presented which fulfills all those requirements. This generalizes the work by [H. Jin & X. Y. Zhou (2008) Behavioral portfolio selection in continuous time, Mathematical Finance 18 (3), 385–426]. Finally, a numerical case study is carried out to illustrate the impact of the utility function and the probability distortion functions.

Keywords: Portfolio choice; behavioral finance; S-shaped utility function; HARA utility; probability distortion (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500454

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