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

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  • Huy N. Chau
  • Andrea Cosso
  • Claudio Fontana
  • Oleksii Mostovyi

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 (NUPBR) and of the finiteness of both primal and dual value functions.

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  • 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.
    • Handle: RePEc:arx:papers:1509.01672
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    2. Jia Yue & Ming-Hui Wang & Nan-Jing Huang, 2022. "Global Optimal Consumption–Portfolio Rules with Myopic Preferences and Loss Aversion," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1427-1455, December.
    3. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    4. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2020. "The value of informational arbitrage," Finance and Stochastics, Springer, vol. 24(2), pages 277-307, April.
    5. Claudio Fontana & Simone Pavarana & Wolfgang J. Runggaldier, 2023. "A stochastic control perspective on term structure models with roll-over risk," Finance and Stochastics, Springer, vol. 27(4), pages 903-932, October.
    6. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio without NFLVR: existence, complete characterization, and duality," Papers 1807.06449, arXiv.org.
    7. 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.
    8. Bálint, Dániel Ágoston, 2022. "Characterisation of L0-boundedness for a general set of processes with no strictly positive element," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 51-75.
    9. Fontana, Claudio, 2018. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1007-1033.
    10. 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.
    11. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    12. Michail Anthropelos & Tianran Geng & Thaleia Zariphopoulou, 2020. "Competition in Fund Management and Forward Relative Performance Criteria," Papers 2011.00838, arXiv.org.
    13. Michael Monoyios, 2020. "Infinite horizon utility maximisation from inter-temporal wealth," Papers 2009.00972, arXiv.org, revised Oct 2020.
    14. Herdegen, Martin & Muhle-Karbe, Johannes, 2019. "Sensitivity of optimal consumption streams," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1964-1992.
    15. Oleksii Mostovyi & Mihai S^irbu, 2017. "Sensitivity analysis of the utility maximization problem with respect to model perturbations," Papers 1705.08291, arXiv.org.
    16. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    17. Claudio Fontana & Simone Pavarana & Wolfgang J. Runggaldier, 2023. "A stochastic control perspective on term structure models with roll-over risk," Papers 2304.04453, arXiv.org, revised Oct 2023.
    18. Michael Monoyios, 2020. "Duality for optimal consumption under no unbounded profit with bounded risk," Papers 2006.04687, arXiv.org, revised Dec 2021.
    19. Huy N. Chau & Miklos Rasonyi, 2016. "On optimal investment with processes of long or negative memory," Papers 1608.00768, arXiv.org, revised Mar 2017.
    20. Oleksii Mostovyi, 2017. "Optimal consumption of multiple goods in incomplete markets," Papers 1705.02291, arXiv.org, revised Jan 2018.
    21. Oleksii Mostovyi, 2020. "Stability of the indirect utility process," Papers 2002.09445, arXiv.org.

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