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L\'{e}vy Process, Proportional Transaction Costs and Foreign Exchange

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  • Obonye Doctor
  • Elias R. Offen
  • Edward M. Lungu

Abstract

We analyse optimal portfolio selection problem of maximizing the utility of an agent who invests in a stock and money market account in the presence of proportional transaction cost $\lambda>0$ and foreign exchange rate. The stock price follows a (generalized) Geometric It\^{o}-L\'{e}vy process. The utility function is $U(c)={c^{p}}/{p}$ for all $c\geq0$, $p

Suggested Citation

  • Obonye Doctor & Elias R. Offen & Edward M. Lungu, 2017. "L\'{e}vy Process, Proportional Transaction Costs and Foreign Exchange," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(5), pages 133-141, October.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:5:p:133
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    References listed on IDEAS

    as
    1. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    2. Liuren Wu, 2006. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1445-1474, May.
    3. Hong Liu, 2004. "Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets," Journal of Finance, American Finance Association, vol. 59(1), pages 289-338, February.
    4. Maxim Bichuch, 2011. "Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs," Papers 1112.2749, arXiv.org.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    6. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
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    More about this item

    Keywords

    It^{o}-L'{e}vy diffusions; Portfolio optimization; foreign exchange; stochastic control; utility functions;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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