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Multiplicative Approximation of Wealth Processes Involving No-Short-Sale Strategies

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Abstract

A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sale 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 utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies.

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  • Constantinos Kardaras & Eckhard Platen, 2008. "Multiplicative Approximation of Wealth Processes Involving No-Short-Sale Strategies," Research Paper Series 240, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:240
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    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.
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    Cited by:

    1. 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.
    2. Christoph Czichowsky, 2012. "Time-Consistent Mean-Variance Portfolio Selection in Discrete and Continuous Time," Papers 1205.4748, arXiv.org.
    3. 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..
    4. 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.
    5. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. 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.
    7. 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.

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