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Growth Optimal Portfolio in a Market Driven by a Jump-Diffusion-Like Process or a Levy Process


  • Jia-an Yan

    () (Inst. of Applied Math., Academy of Mathematics and Systems Science, Academia Sinica)

  • Qiang Zhang

    () (Dept. of Economics and Finance, City University of Hong Kong)

  • Shuguang Zhang

    () (Dept. of Stat. & Finance, University of Science and Technology of China)


It is shown that in a market modeled by a vector-valued semimartingale, when we choose the wealth process of an admissible self-financing strategy as a numeraire such that the historical probability measure becomes a martingale measure, then this numeraire must be the wealth process of a growth optimal portfolio. As applications of this result, the growth optimal portfolio in a market driven by a jump-diffusion-like process or a Levy process is worked out.

Suggested Citation

  • Jia-an Yan & Qiang Zhang & Shuguang Zhang, 2000. "Growth Optimal Portfolio in a Market Driven by a Jump-Diffusion-Like Process or a Levy Process," Annals of Economics and Finance, Society for AEF, vol. 1(1), pages 101-116, May.
  • Handle: RePEc:cuf:journl:y:2000:v:1:i:1:p:101-116

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    More about this item


    Jump-diffusion; Levy process; Martingale measure; Numeraire portfolio; Growth optimal portfolio; Relative entropy;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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