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Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption

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Abstract

We consider the problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of the theory is that the value functions of the primal and dual problems are finite.

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Acknowledgements

This work is part of the author’s PhD thesis. I would like to thank Dmitry Kramkov for being a supportive adivisor, whose suggestions and ideas helped in writing this paper. I would also like to thank Giovanni Leoni, Scott Robertson and Mihai Sîrbu for remarks and discussions.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 1 University Station C 1200, Austin, TX, 78712-0257, USA

    Oleksii Mostovyi

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  1. Oleksii Mostovyi
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Mostovyi, O. Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption. Finance Stoch 19, 135–159 (2015). https://doi.org/10.1007/s00780-014-0248-5

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