An extended Novikov-type criterion for local martingales with jumps

TL;DR

This paper establishes an extended Novikov-type criterion for local martingales with jumps, providing a sufficient condition based on exponential moments of quadratic variations to ensure their exponential martingales are true martingales.

Contribution

It introduces a new criterion extending previous results, applicable to local martingales with nonnegative jumps, based on convex combinations of quadratic variations.

Findings

The criterion guarantees the exponential martingale is true under specified conditions.

It generalizes earlier known criteria for local martingales with jumps.

The result broadens the applicability of Novikov-type conditions.

Abstract

For local martingales with nonnegative jumps, we prove a sufficient criterion for the corresponding exponential martingale to be a true martingale. The criterion is in terms of exponential moments of a convex combination of the optional and predictable quadratic variation. The result extends earlier known criteria.