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 Fo ̈llmer’s measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales. Keywords: Local martingale; stochastic exponential; Fo ̈llmer’s measure; uniform integrability; lower function; Bessel process.
Stochastic Processes and Their Applications, (123)2, 404–421.
Complex Systems, Computation and Language, Computational Finance, and Cyber Risk