IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0903.3736.html
   My bibliography  Save this paper

Num\'{e}raire-invariant preferences in financial modeling

Author

Listed:
  • Constantinos Kardaras

Abstract

We provide an axiomatic foundation for the representation of num\'{e}raire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following choice rule: the agent prefers one outcome over another if and only if the expected (under the agent's subjective probability) relative rate of return of the latter outcome with respect to the former is nonpositive. With the addition of a transitivity requirement, this last preference relation has an extension that can be numerically represented by expected logarithmic utility. We also treat the case of a dynamic environment where consumption streams are the objects of choice. There, a novel result concerning a canonical representation of unit-mass optional measures enables us to explicitly solve the investment--consumption problem by separating the two aspects of investment and consumption. Finally, we give an application to the problem of optimal num\'{e}raire investment with a random time-horizon.

Suggested Citation

  • Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
    • Handle: RePEc:arx:papers:0903.3736
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0903.3736
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Henry Allen Latane, 1959. "Criteria for Choice Among Risky Ventures," Journal of Political Economy, University of Chicago Press, vol. 67(2), pages 144-144.
    2. Paul A. Samuelson, 2011. "Why We Should Not Make Mean Log of Wealth Big Though Years to Act Are Long," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 34, pages 491-493, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Gordan Zitkovic, 2005. "Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment," Papers math/0503516, arXiv.org.
    5. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    6. John Burr Williams, 1936. "Speculation and the Carryover," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 50(3), pages 436-455.
    7. repec:dau:papers:123456789/1803 is not listed on IDEAS
    8. Harold W. Kuhn, 2007. "Introduction to John von Neuman and Oskar Morgenstern's Theory of Games and Economic Behavior," Introductory Chapters, in: Theory of Games and Economic Behavior (Commemorative Edition), Princeton University Press.
    9. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    10. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," Papers math/0503013, arXiv.org, revised May 2006.
    11. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    12. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    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. Song, Shiqi, 2016. "Drift operator in a viable expansion of information flow," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2297-2322.
    2. Beatrice Acciaio & Hans Föllmer & Irina Penner, 2012. "Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles," Finance and Stochastics, Springer, vol. 16(4), pages 669-709, October.
    3. Irina Penner & Anthony Réveillac, 2014. "Risk measures for processes and BSDEs," Post-Print hal-00814702, HAL.

    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. Constantinos Kardaras & Jan Obłój & Eckhard Platen, 2017. "The Numéraire Property And Long-Term Growth Optimality For Drawdown-Constrained Investments," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 68-95, January.
    2. Kardaras, Constantinos, 2010. "Numéraire-invariant preferences in financial modeling," LSE Research Online Documents on Economics 44993, London School of Economics and Political Science, LSE Library.
    3. Baldeaux Jan & Ignatieva Katja & Platen Eckhard, 2014. "A tractable model for indices approximating the growth optimal portfolio," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 1-21, February.
    4. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2013, January-A.
    5. Eckhard Platen & Renata Rendek, 2012. "Approximating the numéraire portfolio by naive diversification," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 34-50, February.
    6. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    7. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    8. Constantinos Kardaras, 2008. "The continuous behavior of the numeraire portfolio under small changes in information structure, probabilistic views and investment constraints," Papers 0804.2912, arXiv.org, revised Nov 2009.
    9. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.
    10. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    11. Di Tella, Paolo, 2020. "On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 760-784.
    12. Md. Azizul Baten & Anton Abdulbasah Kamil, 2013. "Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, March.
    13. Mikhail Zhitlukhin, 2020. "A continuous-time asset market game with short-lived assets," Papers 2008.13230, arXiv.org.
    14. Peter Imkeller & Nicolas Perkowski, 2015. "The existence of dominating local martingale measures," Finance and Stochastics, Springer, vol. 19(4), pages 685-717, October.
    15. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.
    17. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
    18. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    19. Mikhail Zhitlukhin, 2022. "A continuous-time asset market game with short-lived assets," Finance and Stochastics, Springer, vol. 26(3), pages 587-630, July.
    20. Claudio Fontana, 2015. "Weak And Strong No-Arbitrage Conditions For Continuous Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-34.

    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:0903.3736. 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.