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

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  • Oleksii Mostovyi

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. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Oleksii Mostovyi, 2015. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Finance and Stochastics, Springer, vol. 19(1), pages 135-159, January.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:1:p:135-159
    DOI: 10.1007/s00780-014-0248-5
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    Citations

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    Cited by:

    1. Ashley Davey & Michael Monoyios & Harry Zheng, 2021. "Duality for optimal consumption with randomly terminating income," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1275-1314, October.
    2. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    3. Kasper Larsen & Oleksii Mostovyi & Gordan Žitković, 2018. "An expansion in the model space in the context of utility maximization," Finance and Stochastics, Springer, vol. 22(2), pages 297-326, April.
    4. Michael Monoyios & Oleksii Mostovyi, 2022. "Stability of the Epstein-Zin problem," Papers 2208.09895, arXiv.org, revised Apr 2023.
    5. Robert Jarrow, 2018. "An Equilibrium Capital Asset Pricing Model in Markets with Price Jumps and Price Bubbles," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-33, June.
    6. Sigrid Källblad, 2017. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Finance and Stochastics, Springer, vol. 21(2), pages 397-425, April.
    7. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    8. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.
    9. Ashley Davey & Michael Monoyios & Harry Zheng, 2020. "Duality for optimal consumption with randomly terminating income," Papers 2011.00732, arXiv.org, revised May 2021.
    10. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    11. Constantinos Kardaras, 2019. "Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to Mathematical Finance," Papers 1908.03946, arXiv.org, revised Aug 2019.
    12. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    13. Michael Monoyios, 2020. "Infinite horizon utility maximisation from inter-temporal wealth," Papers 2009.00972, arXiv.org, revised Oct 2020.
    14. Oleksii Mostovyi & Mihai S^irbu, 2017. "Sensitivity analysis of the utility maximization problem with respect to model perturbations," Papers 1705.08291, arXiv.org.
    15. Michael Monoyios, 2020. "Duality for optimal consumption under no unbounded profit with bounded risk," Papers 2006.04687, arXiv.org, revised Dec 2021.
    16. Oleksii Mostovyi, 2017. "Optimal consumption of multiple goods in incomplete markets," Papers 1705.02291, arXiv.org, revised Jan 2018.
    17. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    18. Oleksii Mostovyi, 2020. "Stability of the indirect utility process," Papers 2002.09445, arXiv.org.
    19. Robert Jarrow, 2017. "A Capm With Trading Constraints And Price Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-39, December.

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    More about this item

    Keywords

    Utility maximization; Incomplete markets; Duality theory; Legendre–Fenchel transformation; Stochastic clock; 91G10; 93E20; G11;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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