Abstract
We propose some portfolio selection models based on Cumulative Prospect Theory. In particular, we consider alternative probability weighting functions in order to model probability distortion. The resulting mathematical programming problem turns out to be highly non-linear and non-differentiable. So, we adopt a solution approach based on the metaheuristic Particle Swarm Optimization. We select the portfolios under the behavioral approach and perform an application to the European equity market as represented by the STOXX Europe 600 Index and compare their performances.
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Notes
- 1.
Wakker [21] provides a thorough treatment on PT.
- 2.
Tversky and Kahneman [20] estimated these parameters: \(a = b = 0.88\), and \(\lambda =2.25\). We will refer to this set of parameters as TK sentiment.
- 3.
- 4.
See [3].
- 5.
See [16] for a review.
- 6.
Henceforth and in the applications, we will refer to this probability distortion as TK function.
- 7.
In the same article, Prelec derives two other probability weighting functions: the conditionally-invariant exponential-power and the projection-invariant hyperbolic-logarithm function.
- 8.
The CRS weighting function has been adopted by Tversky and Kahneman [16] in a behavioral model for the evaluation of European options.
- 9.
In particular, in the applications we adopt the TK, Prelec, and CRS functions.
- 10.
Three probability weighting functions, times two reference points, times fiftyone out-of-sample weeks.
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Barro, D., Corazza, M., Nardon, M. (2022). Alternative Probability Weighting Functions in Behavioral Portfolio Selection. In: Salvati, N., Perna, C., Marchetti, S., Chambers, R. (eds) Studies in Theoretical and Applied Statistics . SIS 2021. Springer Proceedings in Mathematics & Statistics, vol 406. Springer, Cham. https://doi.org/10.1007/978-3-031-16609-9_9
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