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Minimizing the expected market time to reach a certain wealth level

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  • Constantinos Kardaras
  • Eckhard Platen

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, 2009. "Minimizing the expected market time to reach a certain wealth level," Papers 0904.1903, arXiv.org.
    • Handle: RePEc:arx:papers:0904.1903
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    References listed on IDEAS

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    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. 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.
    3. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    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.
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    Cited by:

    1. 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.
    2. 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..
    3. Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
    4. 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.
    5. Mikhail Zhitlukhin, 2018. "Survival investment strategies in a continuous-time market model with competition," Papers 1811.12491, arXiv.org, revised Sep 2019.
    6. Mikhail Zhitlukhin, 2020. "Asymptotic minimization of expected time to reach a large wealth level in an asset market game," Papers 2007.04909, arXiv.org.
    7. 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.
    8. Eckhard Platen & Renata Rendek, 2017. "Market Efficiency and Growth Optimal Portfolio," Papers 1706.06832, arXiv.org.

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