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01-05-2013 | Symposium

Optimal portfolio choice for a behavioural investor in continuous-time markets

Authors: Miklós Rásonyi, Andrea M. Rodrigues

Published in: Annals of Finance | Issue 2/2013

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Abstract

The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time financial market framework and assuming that asset prices are modelled by semimartingales, we derive sufficient and necessary conditions for the well-posedness of the optimisation problem in the case of piecewise-power probability distortion and utility functions. Finally, under straightforwardly verifiable conditions, we further demonstrate the existence of an optimal strategy.

previous article Utilities bounded below

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Note that it does not necessarily have to be a common stock, it can also be referring to a commodity, a foreign currency, an exchange rate or a market index.

We recall that, for every real number \(x\), the cumulative distribution function of \(\rho \) with respect to the probability measure \(\mathbb Q \) is given by \(F_{\rho }^\mathbb{Q }\!\left(x\right)=\mathbb Q \!\left(\rho \le x\right)\).

Note that here \(x^{+}=\max \left\{ x,0\right\} \) and \(x^{-}=-\min \left\{ x,0\right\} \).

We denote by \(A^{c}\) the complement of \(A\) in \(\varOmega \).

Here \(\fancyscript{B}\!\left(X\right)\) denotes the Borel \(\sigma \)-algebra on the topological space \(X\). A mapping \(K\) from \(\mathbb R \times \fancyscript{B}\!\left(\mathbb R \right)\) into \(\left[0,+\infty \right]\) is called a transition probability kernel on \(\left(\mathbb R ,\fancyscript{B}\!\left(\mathbb R \right)\right)\) if the mapping \(x \mapsto K\!\left(x,B\right)\) is measurable for every set \(B \in \fancyscript{B}\!\left(\mathbb R \right)\), and the mapping \(B \mapsto K\!\left(x,B\right)\) is a probability measure for every \(x \in \mathbb R \).

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Title: Optimal portfolio choice for a behavioural investor in continuous-time markets
Authors: Miklós Rásonyi
Andrea M. Rodrigues
Publication date: 01-05-2013
Publisher: Springer-Verlag
Published in: Annals of Finance / Issue 2/2013
Print ISSN: 1614-2446
Electronic ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-012-0211-4

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