Kazamaki's condition explained

In mathematics, Kazamaki's condition gives a sufficient criterion ensuring that the Doléans-Dade exponential of a local martingale is a true martingale. This is particularly important if Girsanov's theorem is to be applied to perform a change of measure. Kazamaki's condition is more general than Novikov's condition.

Statement of Kazamaki's condition

Let

M=(Mt)t

be a continuous local martingale with respect to a right-continuous filtration

(l{F}t)t

. If

(\exp(Mt/2))t

is a uniformly integrable submartingale, then the Doléans-Dade exponential Ɛ(M) of M is a uniformly integrable martingale.

References

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