Stochastic control for BSDEs and ABSDEs with Markov chain noises

ABSTRACT

In this paper we discuss the control of a stochastic process for which the driving noise is provided by a martingale associated with a Markov chain. A duality between stochastic differential equations and backward stochastic differential equations is used, as well as a duality between stochastic differential delay equations and anticipated backward stochastic differential equations.The proof involves some delicate analysis to establish comparison results.

KEYWORDS:

• Duality between SDEs and BSDEs
• Markov chain noise
• duality between SDDEs and anticipated BSDEs
• stochastic control

Acknowledgements

The authors gratefully acknowledge the help from Prof. Samuel N. Cohen.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research council of Canada and the Australian Research Council.