Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment

He, Xue Dong; Zhou, Xun Yu

doi:10.1287/mnsc.1100.1269

Cited by 243 publications

(69 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…First, modeling the Disposition Effect with respect to Prospect Theory parameters appears to be too restrictive as investors in could also exhibit the opposite Disposition Effect (we refer to Weber et al (2014) for details of our dataset). In addition, 12 It should be noted that modeling portfolio strategies as in Vlcek and Hens (2011) is in line with theoretical models on static portfolio choice under Prospect Theory such as (Schmidt and Zank (2007), Jin and Zhou (2008), Bernard and Ghossoub (2010) and He and Zhou (2011)), who found that investors with Prospect Theory preferences may find corner solutions optimal and prefer full sales of existing positions (see Gomes (2005) for a CRRA-form of Prospect Theory and Polkovnichenko (2005) under rank-dependent Utility). Note that once multiperiod settings are considered, corner solutions are not necessarily optimal any longer (e.g.…”

Section: Prospect Theory: Fit For Finance? a Brief Reflection Of Relementioning

confidence: 69%

Taming Models of Prospect Theory in the Wild? Estimation of Vlcek and Hens (2011)

2016

View full text Add to dashboard Cite

Abstract. Shortcomings revealed by experimental and theoretical researchers such as Allais (1953), Rabin (2000) and Rabin and Thaler (2001) that put the classical expected utility paradigm von Neumann and Morgenstern (1947) into question, led to the proposition of alternative and generalized utility functions, that intend to improve descriptive accuracy. The perhaps best known among those alternative preference theories, that has attracted much popularity among economists, is the so called Prospect Theory by Kahneman and Tversky (1979) and Tversky and Kahneman (1992). Its distinctive features, governed by its set of risk parameters such as risk sensitivity, loss aversion and decision weights, stimulated a series of economic and financial models that build on the previously estimated parameter values by Tversky and Kahneman (1992) to analyze and explain various empirical phenomena for which expected utility doesn't seem to offer a satisfying rationale. In this paper, after providing a brief overview of the relevant literature, we take a closer look at one of those papers, the trading model of Vlcek and Hens (2011) and analyze its implications on Prospect Theory parameters using an adopted maximum likelihood approach for a dataset of 656 individual investors from a large German discount brokerage firm. We find evidence that investors in our dataset are moderately averse to large losses and display high risk sensitivity, supporting the main assumptions of Prospect Theory.

show abstract

Section: Prospect Theory: Fit For Finance? a Brief Reflection Of Relementioning

confidence: 69%

Taming Models of Prospect Theory in the Wild? Estimation of Vlcek and Hens (2011)

2016

View full text Add to dashboard Cite

show abstract

“…22 However, contrary to the case when Ω > 0 the household does not reduce the consumption gap but widens this gap. This means that the household increases its consumption even more than the Joneses do.…”

Section: (Iv) Limmentioning

confidence: 92%

The consumption–investment decision of a prospect theory household: A two-period model

Hlouskova

Fortin

Tsigaris

2017

Journal of Mathematical Economics

View full text Add to dashboard Cite

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis study extends the literature on portfolio choice under prospect theory preferences by introducing a two-period life cycle model, where the household decides on optimal consumption and investment in a portfolio with one risk-free and one risky asset. The optimal solution depends primarily on the household's choice of the present value of the consumption reference levels relative to the present value of its endowment income. If the present value of the consumption reference levels is set below the present value of endowment income, then the household behaves in such a way to avoid relative losses in consumption in any present or future state of nature (good or bad). As a result the degree of loss aversion does not directly affect optimal consumption and risk taking activity. However, it must be sufficiently high in order to rule out outcomes with relative losses. On the other hand, if the present value of the consumption reference levels is set exactly equal to the present value of the endowment income, i.e., the household sets its reference levels such that they are in balance with its income, then the household's optimal consumption is the reference consumption in both periods and the household will not invest in the risky asset. Finally, if the present value of the household's consumption reference levels is set above the present value of its endowment income, then the household cannot avoid experiencing a relative loss in consumption, either now or in the future. As a result, loss aversion directly affects consumption and risky investment. Reference levels play a significant role in consumption and risk taking activity. In most cases the household will "follow the Joneses" if the reference levels are set equal to the consumption levels of the Joneses. Independent of how consumption reference levels are set, being more ambitious, i.e., increasing one's reference levels, will result in less happiness. The only case when this is not true is when reference levels increase with growing income (and the present value of reference levels is set below the present value of endowment income).

show abstract

“…Use of benchmark tracking in portfolio selection and management can be found in [Gaivoronski, Krylov & van der Wijst, 2005] and [Lioui & Poncet, 2013]. Similarly, use of reference points in portfolio selection and dependence of the optimal risky exposure on the reference point is in [He & Zhou, 2011]. Penalty costs and benchmark targets in pension funds optimization appear in [Geyer & Ziemba, 2008].…”

Section: The Modelmentioning

confidence: 99%

Income drawdown option with minimum guarantee

Giacinto

Federico

Gozzi

et al. 2014

European Journal of Operational Research

View full text Add to dashboard Cite

This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement.This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider, as a first step, the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. We extend their model by adding a no short-selling constraint on the control variable and a final capital requirement constraint on the state variable. This implies, in particular, no ruin.The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We write the non-linear Hamilton-Jacobi-Bellman equation for the problem and transform it into a dual one that is semi-linear, following a well-established duality procedure. In the special relevant case without running cost, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.J.E.L. classification: C61, G11, G23. A.M.S. classification: 91B28, 93E20, 49L25.Keywords: pension fund, decumulation phase, constrained portfolio, stochastic optimal control, dynamic programming, Hamilton-Jacobi-Bellman equation. Acknowledgements:We thank three anonymous reviewers for thorough reading and the editor for careful handling of the paper.

show abstract

Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment

Cited by 243 publications

References 21 publications

Taming Models of Prospect Theory in the Wild? Estimation of Vlcek and Hens (2011)

Taming Models of Prospect Theory in the Wild? Estimation of Vlcek and Hens (2011)

The consumption–investment decision of a prospect theory household: A two-period model

Income drawdown option with minimum guarantee

Contact Info

Product

Resources

About