The finiteness of moments of a stochastic exponential

Bronius Grigelionis and Vigirdas Mackevicius

Statistics & Probability Letters, 2003, vol. 64, issue 3, 243-248

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.

Keywords: Stochastic; exponential; Girsanov; theorem (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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