Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise

Abstract

Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with Markov chain noise, adapting previous results under simplified hypotheses. We introduce a type of nonlinear expectation, the $f$-expectation, which is an interpretation of the solution to a BSDE, and use it to establish a converse comparison theorem for the same type of equations as those in the comparison results.