IDEAS home Printed from https://ideas.repec.org/p/arx/papers/math-0702727.html
   My bibliography  Save this paper

On Robust Utility Maximization

Author

Listed:
  • Traian A Pirvu
  • Ulrich G Haussmann

Abstract

This paper studies the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be achieved for logartihmic utility, otherwise a cashflow should be added to the investor s wealth. The cashflow can be decomposed into the sum of an increasing and a decreasing process. The last one can be viewed as consumption. The first one is an insurance premium the agent has to pay.

Suggested Citation

  • Traian A Pirvu & Ulrich G Haussmann, 2007. "On Robust Utility Maximization," Papers math/0702727, arXiv.org.
    • Handle: RePEc:arx:papers:math/0702727
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/math/0702727
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gordan Zitkovic, 2005. "Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment," Papers math/0503516, arXiv.org.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    4. Levhari, David & Mirman, Leonard J, 1977. "Savings and Consumption with an Uncertain Horizon," Journal of Political Economy, University of Chicago Press, vol. 85(2), pages 265-281, April.
    5. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
    6. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    7. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    Full references (including those not matched with items on IDEAS)

    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. Zeckhauser, Richard Jay & Tran, Ngoc-Khanh, 2011. "The Behavior of Savings and Asset Prices When Preferences and Beliefs are Heterogeneous," Scholarly Articles 5027955, Harvard Kennedy School of Government.
    2. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    3. Basak, Suleyman, 2000. "A model of dynamic equilibrium asset pricing with heterogeneous beliefs and extraneous risk," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 63-95, January.
    4. Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
    5. Ramser, Hans Jürgen, 1977. "Lebenszyklustheorie des Sparens: Zum Stand der Theorie," Discussion Papers, Series I 101, University of Konstanz, Department of Economics.
    6. Hui Chen & Jianjun Miao & Neng Wang, 2010. "Entrepreneurial Finance and Nondiversifiable Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(12), pages 4348-4388, December.
    7. Axel H. Börsch-Supan & Tabea Bucher-Koenen & Michael D. Hurd & Susann Rohwedder, 2018. "Saving Regret," NBER Working Papers 25238, National Bureau of Economic Research, Inc.
    8. Ivar Ekeland & Traian A. Pirvu, 2007. "Investment and Consumption without Commitment," Papers 0708.0588, arXiv.org.
    9. Jianjun Miao & Neng Wang, 2004. "Investment, Hedging, and Consumption Smoothing," Finance 0407014, University Library of Munich, Germany.
    10. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2015. "Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation," Finance and Stochastics, Springer, vol. 19(2), pages 415-448, April.
    11. 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.
    12. Ivar Ekeland & Traian A Pirvu, 2008. "On a Non-Standard Stochastic Control Problem," Papers 0806.4026, arXiv.org.
    13. Frederic Cherbonnier, 2016. "optimal insurance for time-inconsistent agents," 2016 Meeting Papers 1344, Society for Economic Dynamics.
    14. Oleksii Mostovyi, 2011. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Papers 1107.5852, arXiv.org, revised Jul 2012.
    15. Haavio, Markus & Kotakorpi, Kaisa, 2011. "The political economy of sin taxes," European Economic Review, Elsevier, vol. 55(4), pages 575-594, May.
    16. Ana Paula MARTINS, 2016. "Wealth-In-Utility and Time-Consistent Growth: Real Excursions with an “Overlapping” Welfare Function," Turkish Economic Review, KSP Journals, vol. 3(1), pages 54-81, March.
    17. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    18. 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.
    19. Hong Yan, 2009. "Estimation Uncertainty and the Equity Premium," International Review of Finance, International Review of Finance Ltd., vol. 9(3), pages 243-268, September.
    20. Arthur Hau, 2001. "Precautionary Saving and Mortality-Contingent Social Insurance Programs," Public Finance Review, , vol. 29(1), pages 61-82, January.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:math/0702727. See general information about how to correct material in RePEc.

    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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.