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Optimal Novikov-type criteria for local martingales with jumps


 
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1. Title Title of document Optimal Novikov-type criteria for local martingales with jumps
 
2. Creator Author's name, affiliation, country Alexander Sokol; University of Copenhagen; Denmark
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Martingale, Exponential martingale, Uniform integrability, Novikov, Optimal, Poisson process
 
3. Subject Subject classification 60G44
 
4. Description Abstract

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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-05-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2312
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2312
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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