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Optimal consumption of multiple goods in incomplete markets

Part of: Mathematical finance Stochastic systems and control

Published online by Cambridge University Press:  16 November 2018

Oleksii Mostovyi
Oleksii Mostovyi*
Affiliation:
University of Connecticut
*
* Postal address: Department of Mathematics, University of Connecticut, 341 Mansfield Road U1009, Storrs, CT 06269-1009, USA. Email address: oleksii.mostovyi@uconn.edu
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Abstract

We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.

Keywords

Optimal consumptionmultiple goodsutility maximizationno unbounded profit with bounded riskarbitrage of the first kindlocal martingale deflatorduality theorysemimartingaleincomplete marketoptimal investment

MSC classification

Primary: 91G10: Portfolio theory 93E20: Optimal stochastic control

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 3 , September 2018 , pp. 810 - 822
Copyright
Copyright © Applied Probability Trust 2018 

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