IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i6p1964-1992.html
   My bibliography  Save this article

Sensitivity of optimal consumption streams

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918303028
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2018.06.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. 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.
    3. Oleksii Mostovyi, 2017. "Optimal Investment With Intermediate Consumption And Random Endowment," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 96-114, January.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    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. Kasper Larsen & H. Mete Soner & Gordan Zitkovic, 2014. "Facelifting in Utility Maximization," Papers 1404.2227, arXiv.org.
    11. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    12. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    13. 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.
    14. Jan Kallsen & Shen Li, 2013. "Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach," Papers 1309.3479, arXiv.org.
    15. Peter O. Christensen & Kasper Larsen, 2014. "Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility," Review of Asset Pricing Studies, Oxford University Press, vol. 4(2), pages 247-285.
    16. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 82(3), pages 465-473.
    17. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    18. 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.
    19. Kasper LARSEN & Mete SONER & Gordan ZITKOVIC, 2014. "Facelifting in Utility Maximization," Swiss Finance Institute Research Paper Series 14-61, Swiss Finance Institute.
    20. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    21. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Transaction Costs," Working Papers hal-01711371, HAL.
    3. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium Returns with Transaction Costs," Post-Print hal-01569408, HAL.
    4. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Utility Maximization with Small Transaction Costs," Papers 1802.06120, arXiv.org, revised Mar 2021.
    5. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium returns with transaction costs," Finance and Stochastics, Springer, vol. 22(3), pages 569-601, July.
    6. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
    7. Erhan Bayraktar & Thomas Cayé & Ibrahim Ekren, 2021. "Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 36-108, January.
    8. Lukas Gonon & Johannes Muhle-Karbe & Xiaofei Shi, 2019. "Asset Pricing with General Transaction Costs: Theory and Numerics," Papers 1905.05027, arXiv.org, revised Apr 2020.
    9. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org, revised Mar 2015.
    10. Andrew B. Abel & Stavros Panageas, 2020. "Precautionary Saving in a Financially-Constrained Firm," NBER Working Papers 26628, National Bureau of Economic Research, Inc.
    11. Emilio Fernandez-Corugedo, 2004. "Consumption Theory," Handbooks, Centre for Central Banking Studies, Bank of England, number 23.
    12. Bruno Bouchard & Ludovic Moreau & Mete Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    13. 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.
    14. Marzia De Donno & Mario Menegatti, 2020. "Some conditions for the equivalence between risk aversion, prudence and temperance," Theory and Decision, Springer, vol. 89(1), pages 39-60, July.
    15. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    16. 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.
    17. Michael Monoyios, 2010. "Utility-Based Valuation and Hedging of Basis Risk With Partial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 519-551.
    18. Mostovyi, Oleksii, 2020. "Asymptotic analysis of the expected utility maximization problem with respect to perturbations of the numéraire," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4444-4469.
    19. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.
    20. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:129:y:2019:i:6:p:1964-1992. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.