Optimal Novikov-type criteria for local martingales with jumps. (English) Zbl 1312.60051

Summary: We consider cadlag local martingales \(M\) with initial value zero and jumps larger than \(a\) for some \(a\) larger than or equal to \(-1\), and prove Novikov-type criteria for an exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a corollary, we obtain a verbatim extension of the classical Novikov criterion for continuous local martingales to the case of local martingales with initial value zero and nonnegative jumps.


60G44 Martingales with continuous parameter
60G40 Stopping times; optimal stopping problems; gambling theory
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