A new proof for the conditions of Novikov and Kazamaki

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Ruf, Johannes^1,2 

[1] Univ Oxford, Oxford Man Inst Quantitat Finance, Oxford OX1 2JD, England

[2] Univ Oxford, Math Inst, Oxford OX1 2JD, England

关键词: Local martingale;    Stochastic exponential;    Follmer's measure;    Uniform integrability;    Lower function;    Bessel process;   

DOI  :  10.1016/j.spa.2012.09.011

来源: Elsevier

【 摘 要 】

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 Follmer's measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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