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Optimal investment with intermediate consumption under no unbounded profit with bounded risk

Part of: Mathematical finance Stochastic systems and control

Published online by Cambridge University Press:  15 September 2017

Huy N. Chau ,
Andrea Cosso ,
Claudio Fontana  and
Oleksii Mostovyi
Huy N. Chau*
Affiliation:
Hungarian Academy of Sciences
Andrea Cosso*
Affiliation:
Politecnico di Milano
Claudio Fontana*
Affiliation:
Paris Diderot University
Oleksii Mostovyi*
Affiliation:
University of Connecticut
*
* Postal address: Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Realtanoda utca 13-15, H-1053 Budapest, Hungary. Email address: chau@renyi.hu
** Postal address: Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy. Email address: andrea.cosso@polimi.it
*** Postal address: Laboratoire de Probabilités et Modèles Aléatoires, Paris Diderot University, av. de France, 75205 Paris, France. Email address: fontana@math.univ-paris-diderot.fr
**** Postal address: Department of Mathematics, University of Connecticut, U1009, 341 Mansfield Road, Storrs, CT 06269-1009, USA. Email address: oleksii.mostovyi@uconn.edu
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Abstract

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk and of the finiteness of both primal and dual value functions.

Keywords

Utility maximizationarbitrage of the first kindlocal martingale deflatorduality theorysemimartingaleincomplete market

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 93E20: Optimal stochastic control
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 710 - 719
Copyright
Copyright © Applied Probability Trust 2017 

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