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

  • Huy N. Chau (a1), Andrea Cosso (a2), Claudio Fontana (a3) and Oleksii Mostovyi (a4)

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.

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Corresponding author

* 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

References

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