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The finiteness of moments of a stochastic exponential

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  • Grigelionis, Bronius
  • Mackevicius, Vigirdas

Abstract

It is well known that the stochastic exponential , of a continuous local martingale M has expectation EZt=1 and, thus, is a martingale if (Novikov's condition). We show that, for p>1, EZtp t} 0. As a consequence, we get that the moments of the stochastic exponential of a stochastic integral with respect to a Brownian motion are all finite, provided the integrand is a Brownian functional of linear growth.

Suggested Citation

  • Grigelionis, Bronius & Mackevicius, Vigirdas, 2003. "The finiteness of moments of a stochastic exponential," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 243-248, September.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:3:p:243-248
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    References listed on IDEAS

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    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
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    2. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.

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