nach oben

Annals of Finance

Erschienen in:

01.05.2013 | Symposium

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

verfasst von: Miklós Rásonyi, Andrea M. Rodrigues

Erschienen in: Annals of Finance | Ausgabe 2/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

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.

Vorheriger Artikel Utilities bounded below

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

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 \(x \in \mathbb R \).

Berkelaar, A.B., Kouwenberg, R., Post, T.: Optimal portfolio choice under loss aversion. Rev Econ Stat 86(4), 973–987 (2004)CrossRef

Bernard, C., Ghossoub, M.: Static portfolio choice under cumulative prospect theory. Math Financ Econ 2, 277–306 (2010)CrossRef

Borkar, V.S.: Probability Theory: An Advanced Course. Berlin: Springer (1995)

Campi, L., Del Vigna, M.: Weak insider trading and behavioural finance. SIAM J Financ Math 3, 242–279 (2012)CrossRef

Carassus, L., Rásonyi, M.: On optimal investment for a behavioural investor in multiperiod incomplete market models. Preprint version 1. Forthcoming in Math Finance. (2011) Available online at http://arxiv.org/abs/1107.1617

Carlier, G., Dana, R.-A.: Optimal demand for contingent claims when agents have law invariant utilities. Math Financ 21, 169–201 (2011)

Harrison, J.M., Pliska, S.R.: Martingales and stochastic integrals in the theory of continuous trading. Stoch Process Appl 11, 215–260 (1981)CrossRef

He, X.D., Zhou, X.Y.: Portfolio choice under cumulative prospect theory: an analytical treatment. Manag Sci 57(2), 315–331 (2011)CrossRef

Jin, H., Zhou, X.Y.: Behavioral portfolio selection in continuous time. Math Financ 18, 385–426 (2008)CrossRef

Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–292 (1979)CrossRef

Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance, Applications of Mathematics., vol. 39, 2nd edn. Berlin: Springer (1998)

Kast, R., Lapied, A., Toquebeuf, P.: Updating choquet integrals, consequentialism and dynamic consistency. In: ICER Working Papers—Applied Mathematics Series. Available at http://ideas.repec.org/p/icr/wpmath/04-2008.html (2008)

Prokhorov, Y.V.: Convergence of random processes and limit theorems in probability theory. Theor Probab Appl 1(2), 157–214 (1956)CrossRef

Rásonyi, M., Stettner, L.: On the utility maximization problem in discrete-time financial market models. Ann Appl Probab 15, 1367–1395 (2005)CrossRef

Reichlin, C.: Non-concave utility maximization with a given pricing measure. Available at SSRN http://ssrn.com/abstract=1940277 (2011)

Schachermayer, W.: Optimal investment in incomplete markets when wealth may become negative. Ann Appl Probab 11(3), 694–734 (2001)CrossRef

Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5, 297–323 (1992)CrossRef

von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, 2nd edn. Princeton: Princeton University Press (1953)

Titel: Optimal portfolio choice for a behavioural investor in continuous-time markets
verfasst von: Miklós Rásonyi
Andrea M. Rodrigues
Publikationsdatum: 01.05.2013
Verlag: Springer-Verlag
Erschienen in: Annals of Finance / Ausgabe 2/2013
Print ISSN: 1614-2446
Elektronische ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-012-0211-4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2013

Taming animal spirits: risk management with behavioural factors

Inference for systems of stochastic differential equations from discretely sampled data: a numerical maximum likelihood approach

Introduction: behavioral and evolutionary finance

Utilities bounded below

Currency returns, market regimes and behavioral biases

Risk classes for structured products: mathematical aspects and their implications on behavioral investors