A new proof for the conditions of Novikov and Kazamaki

Abstract

This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov's condition and Kazamaki's criterion follow directly from the existence of Föllmer's measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales.

Addendum included

References in corpus (4)

• Equivalent and absolutely continuous measure changes for jump-diffusion processes
• On optimal arbitrage
• Conditioned Martingales
• On the Hedging of Options On Exploding Exchange Rates

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• On the Hedging of Options On Exploding Exchange Rates
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• A few comments on a result of A. Novikov and Girsanov's theorem
• Simplified calculus for semimartingales: Multiplicative compensators and changes of measure
• A Weak Convergence Criterion Constructing Changes of Measure
• Martingale Property in Terms of Semimartingale Problems
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