Malliavin calculus for Markov chains using perturbations of time

Abstract

In this article, we develop a Malliavin calculus associated to a time-continuous Markov chain with finite state space. We apply it to get a criterion of density for solutions of stochastic differential equation involving the Markov chain and also to compute greeks.

Keywords:

• Dirichlet form
• integration by parts formula
• Malliavin calculus
• Markov chain
• computation of greeks

AMS Subject Classifications:

• 60H07
• 60J10
• 60G55
• 91B70

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of T. M. Nguyen benefited from the support of the ‘Chair Markets in Transition’ under the aegis of Louis Bachelier laboratory, a joint initiative of École Polytechnique, Université d’Évry Val d’Essonne and Fédération Bancaire Française.