Making prospect theory fit for finance

Abstract

This paper gives a survey over a common aspect of prospect theory that occurred to be of importance in a series of recent papers developed by Enrico De Giorgi, Thorsten Hens, Janos Mayer, Haim Levy, Thierry Post, Marc Oliver Rieger and Mei Wang. The common aspect of these papers is that the value function of the prospect theory of Kahneman and Tversky (1979) and similarly that of Tversky and Kahneman (1992) has to be re-modelled if one wants to apply it to portfolio selection. Instead of the piecewise power value function, a piecewise negative exponential function should be used. This functional form is still compatible with laboratory experiments but it has the following advantages over and above Kahneman and Tversky`s piecewise power function:1. The Bernoulli Paradox does not arise for lotteries with finite expected value. 2. No infinite leverage/robustness problem arises. 3. CAPM-equilibria with heterogeneous investors and prospect utility do exist. 4. It is able to simultaneously resolve the following asset pricing puzzles: the equity premium, the value and the size puzzle.

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

“…Exemplarily, Rieger and Wang (2008) refined Prospect Theory for the application in continuous-outcome-environments as it is common to model financial markets and assets using stochastic calculus. In DeGiorgi and Hens (2006), the authors discuss the idea of a piecewise negative exponential value function (see DeGeorgi et al (2004)) to capture trading patterns such as the Disposition Effect. They argue that given the power function as used in Vlcek and Hens (2011), investors would not chose to invest in risky assets at the beginning, however, under a piecewise negative exponential value function, the optimal solution can generate a trading pattern similar to the Disposition Effect.…”

“…Despite the work of DeGeorgi et al (2004), DeGiorgi and Hens (2006), Kyle et al (2006) and Rieger and Wang (2008), Prospect Theory with fixed reference points and a power functional is still the most-commonly used functional form in financial studies, backed by recent studies that deal with the best fitting shape (Wakker (2008)). For instance, Blondel (2002) fitted linear, power and exponential functions to experimental data.…”

The expo-power value function as a candidate for the work-horse specification in parametric versions of cumulative prospect theory

“…For example De Giorgi and Hens (2006) consider some applications in portfolio theory. They demonstrate that the power value function leads to the non-existence of equilibrium and suggest the exponential function as an alternative.…”

On the Applicability of Maximum Likelihood Methods: From Experimental to Financial Data

“…Furthermore, for EU T and RDU we use the denotation CRRA for utility functionals with constant relative risk aversion and EXP O to denote exponential power utility functions (Saha (1993)). For SP T and CP T , we use the denotation P OW R to indicate models with kinked power-functionals and CRRA if a power functional used to specify the prospect value functional (Gomes (2005)), where in addition DHG0 denotes value functionals as defined in DeGiorgi and Hens (2006). Quiggin (1982), Tversky and Kahneman (1992) with decision-weightings according to Quiggin (1982) (QU82 ) and Tversky and Kahneman (1992) (KT92 ), regarding the utility functional, we use CRRA and EXPO.…”

“…As for the SPT case, we use a decision weight according to Quiggin (1982) and Tversky and Kahneman (1992) for the CPT function. For SPT and CPT, we specified the functional form of the value functional according to a power function (Kahneman and Tversky (1979)) and contrast the results with an CRRA functional (as in and Gomes (2005)), exponential power functional (EXPO) and a piecewise negative exponential power functional (DGH0 ) as defined in DeGiorgi and Hens (2006). Table (1) provides an overview of the utility models used and their parameter settings in this simulation study.…”