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, extending and generalizing previous work under natural and simplified hypotheses, and establish a converse comparison theorem for the same type of equation after giving the definition and properties of a type of nonlinear expectation: $f$-expectation.

16 pages

References in corpus (1)

• A converse comparison theorem for backward stochastic differential equations with jumps

Cited by in corpus (2)

• Some Properties of Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model
• Backward Stochastic Differential Equations with Continuous Coefficients in a Markov Chain Model and with Applications to European Options