IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/230.html
   My bibliography  Save this paper

Minimizing the Expected Market Time to Reach a Certain Wealth Level

Author

Abstract

In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Ito market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor’s point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.

Suggested Citation

  • Constantinos Kardaras & Eckhard Platen, 2008. "Minimizing the Expected Market Time to Reach a Certain Wealth Level," Research Paper Series 230, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:230
    as

    Download full text from publisher

    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp-230.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    3. Kardaras, Constantinos & Platen, Eckhard, 2011. "On the semimartingale property of discounted asset-price processes," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2678-2691, November.
    4. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    5. Constantinos Kardaras & Eckhard Platen, 2008. "On Financial Markets where only Buy-And-Hold Trading is Possible," Research Paper Series 213, Quantitative Finance Research Centre, University of Technology, Sydney.
    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. Eckhard Platen & Renata Rendek, 2017. "Market Efficiency and Growth Optimal Portfolio," Papers 1706.06832, arXiv.org.
    2. Mikhail Zhitlukhin, 2018. "Survival investment strategies in a continuous-time market model with competition," Papers 1811.12491, arXiv.org, revised Sep 2019.
    3. Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
    4. Mikhail Zhitlukhin, 2020. "Asymptotic minimization of expected time to reach a large wealth level in an asset market game," Papers 2007.04909, arXiv.org.
    5. Sergio Ortobelli Lozza & Enrico Angelelli & Alda Ndoci, 2019. "Timing portfolio strategies with exponential Lévy processes," Computational Management Science, Springer, vol. 16(1), pages 97-127, February.
    6. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," 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 28, pages 409-426, World Scientific Publishing Co. Pte. Ltd..
    7. Paolo Guasoni & Jan Obłój, 2016. "The Incentives Of Hedge Fund Fees And High-Water Marks," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 269-295, April.
    8. Sergio Ortobelli Lozza & Enrico Angelelli & Daniele Toninelli, 2011. "Set-Portfolio Selection with the Use of Market Stochastic Bounds," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 47(0), pages 5-24, November.

    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. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," 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 28, pages 409-426, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. 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.
    4. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    5. Jörn Sass & Manfred Schäl, 2014. "Numeraire portfolios and utility-based price systems under proportional transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 195-234, October.
    6. Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    7. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    8. Hardy Hulley & Shane Miller & Eckhard Platen, 2005. "Benchmarking and Fair Pricing Applied to Two Market Models," Research Paper Series 155, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Martin Herdegen, 2017. "No-Arbitrage In A Numéraire-Independent Modeling Framework," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 568-603, April.
    10. Ashkan Nikeghbali & Eckhard Platen, 2008. "On honest times in financial modeling," Papers 0808.2892, arXiv.org.
    11. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Ke Du & Eckhard Platen, 2016. "Benchmarked Risk Minimization," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 617-637, July.
    13. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    15. 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.
    16. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    18. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    19. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

    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:uts:rpaper:230. 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: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    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.