Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps

2014/11/23 by Martin Larsson, Johannes Ruf, Larsson, Martin +1
Economics, Econometrics and Finance · Mathematics · #60G30 #60G44 #Advanced Harmonic Analysis Research #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 60G07 #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G07 #msc:60G17 #msc:60G30 #msc:60G44 #secondary: 60G17

paper · pdf · doi:10.48550/arxiv.1411.6229

arxiv created 2014/11/23 · openalex publication_date 2014/11/23 · arxiv updated 2014/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of extended local integrability plays a key role. We then apply these characterizations to provide a novel proof for the sufficiency and necessity of Novikov-Kazamaki type conditions for the martingale property of nonnegative local martingales with jumps.

Citations

• Martingale property of exponential semimartingales: a note on explicit conditions and applications to financial models

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