IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0812.0033.html
   My bibliography  Save this paper

Multiplicative approximation of wealth processes involving no-short-sale strategies via simple trading

Author

Listed:
  • Constantinos Kardaras
  • Eckhard Platen

Abstract

A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies.

Suggested Citation

  • Constantinos Kardaras & Eckhard Platen, 2008. "Multiplicative approximation of wealth processes involving no-short-sale strategies via simple trading," Papers 0812.0033, arXiv.org, revised Mar 2010.
    • Handle: RePEc:arx:papers:0812.0033
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0812.0033
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    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. Paul Gassiat & Huyên Pham & Mihai Sîrbu, 2012. "Optimal Investment On Finite Horizon With Random Discrete Order Flow In Illiquid Markets," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 15, pages 349-372, World Scientific Publishing Co. Pte. Ltd..
    2. Paul Gassiat & Huyen Pham & Mihai Sirbu, 2009. "Optimal investment on finite horizon with random discrete order flow in illiquid markets," Papers 0907.2203, arXiv.org.
    3. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    4. Paul Gassiat & Huyên Pham & Mihai Sîrbu, 2011. "Optimal Investment On Finite Horizon With Random Discrete Order Flow In Illiquid Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 17-40.
    5. 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.
    6. Christoph Czichowsky, 2012. "Time-Consistent Mean-Variance Portfolio Selection in Discrete and Continuous Time," Papers 1205.4748, arXiv.org.
    7. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.

    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. Kreher, Dörte, 2017. "Change of measure up to a random time: Details," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1565-1598.
    2. Constantinos Kardaras, 2009. "Finitely additive probabilities and the Fundamental Theorem of Asset Pricing," Papers 0911.5503, arXiv.org.
    3. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    4. Peter Imkeller & Nicolas Perkowski, 2015. "The existence of dominating local martingale measures," Finance and Stochastics, Springer, vol. 19(4), pages 685-717, October.
    5. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Post-Print hal-02373296, HAL.
    6. Kardaras, Constantinos, 2013. "On the closure in the Emery topology of semimartingale wealth-process sets," LSE Research Online Documents on Economics 44996, London School of Economics and Political Science, LSE Library.
    7. Czichowsky, Christoph Johannes & Peyre, Rémi & Schachermayer, Walter & Yang, Junjian, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," LSE Research Online Documents on Economics 85230, London School of Economics and Political Science, LSE Library.
    8. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, arXiv.org, revised Sep 2022.
    9. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
    10. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Finance and Stochastics, Springer, vol. 22(1), pages 161-180, January.
    11. Song, Shiqi, 2016. "Drift operator in a viable expansion of information flow," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2297-2322.
    12. Oliver Janke & Qinghua Li, 2015. "Portfolio Optimization under Shortfall Risk Constraint," Papers 1501.07480, arXiv.org, revised Apr 2016.
    13. Czichowsky, Christoph & Schachermayer, Walter, 2017. "Portfolio optimisation beyond semimartingales: shadowprices and fractional Brownian motion," LSE Research Online Documents on Economics 67689, London School of Economics and Political Science, LSE Library.
    14. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    15. Martin Herdegen & Martin Schweizer, 2016. "Strong Bubbles And Strict Local Martingales," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-44, June.
    16. Christoph Czichowsky & R'emi Peyre & Walter Schachermayer & Junjian Yang, 2016. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Papers 1608.01415, arXiv.org.
    17. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382, arXiv.org, revised Jul 2016.
    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. Leunglung Chan & Eckhard Platen, 2010. "Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model," Papers 1007.2968, arXiv.org, revised Jan 2011.
    20. Dániel Ágoston Bálint & Martin Schweizer, 2019. "Properly Discounted Asset Prices Are Semimartingales," Swiss Finance Institute Research Paper Series 19-53, Swiss Finance Institute.

    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:0812.0033. 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.