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Sensitivity of optimal consumption streams

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  • Herdegen, Martin
  • Muhle-Karbe, Johannes

Abstract

We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. At the leading order, the consumption adjustment does not matter: any choice that matches the budget constraint simply shifts the original utility by the marginal value of the perturbation. Nontrivial results can be obtained by considering the next-to-leading order. Here, one first solves the problem for a deterministic perturbation, which leads to a “prognosis measure”. The desired consumption adjustment for a general endowment perturbation is in turn given by the conditional expectation of the latter, computed under this measure and appropriately weighted with the conditional expectations of the remaining risk-tolerance.

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  • Herdegen, Martin & Muhle-Karbe, Johannes, 2019. "Sensitivity of optimal consumption streams," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1964-1992.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:6:p:1964-1992
    DOI: 10.1016/j.spa.2018.06.011
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    References listed on IDEAS

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    1. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    2. Oleksii Mostovyi, 2017. "Optimal Investment With Intermediate Consumption And Random Endowment," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 96-114, January.
    3. Dylan Possamai & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
    4. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2017. "Trading With Small Price Impact," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 350-400, April.
    5. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    6. Jan Kallsen & Johannes Muhle-Karbe, 2017. "The General Structure Of Optimal Investment And Consumption With Small Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 659-703, July.
    7. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    8. Jan Kallsen & Shen Li, 2013. "Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach," Papers 1309.3479, arXiv.org.
    9. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    10. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    11. Kasper LARSEN & Mete SONER & Gordan ZITKOVIC, 2014. "Facelifting in Utility Maximization," Swiss Finance Institute Research Paper Series 14-61, Swiss Finance Institute.
    12. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    13. 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.
    14. 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.
    15. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    16. Kasper Larsen & H. Mete Soner & Gordan Zitkovic, 2014. "Facelifting in Utility Maximization," Papers 1404.2227, arXiv.org.
    17. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    18. Peter O. Christensen & Kasper Larsen, 2014. "Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 4(2), pages 247-285.
    19. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    20. Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1606-1620, November.
    21. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
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    Cited by:

    1. David Hobson & Martin Herdegen & Joseph Jerome, 2021. "The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utility," Papers 2107.06593, arXiv.org.
    2. Martin Herdegen & David Hobson & Joseph Jerome, 2023. "The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations," Finance and Stochastics, Springer, vol. 27(1), pages 127-158, January.
    3. Martin Herdegen & David Hobson & Joseph Jerome, 2021. "Proper solutions for Epstein-Zin Stochastic Differential Utility," Papers 2112.06708, arXiv.org.

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