Mimicking the marginal distributions of a semimartingale

2009/10/21 by Amel Bentata, Bentata, Amel, Rama Cont +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #60H10 #60J75 #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0910.3992

openalex publication_date 2009/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale ξ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of ξ. Our construction applies to a large class of semimartingales, including smooth functions of a Markov process. We use this result to derive a partial integro-differential equation for the one-dimensional distributions of a semimartingale, extending the Kolmogorov forward equation to a non-Markovian setting.

Cited by

• Short-time asymptotics for marginal distributions of semimartingales
• On the Weak Error for Local Stochastic Volatility Models
• Markovian projections for functionals of Itô semimartingales with jumps

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