Elliott, RobertCohen, Samuel N2012-06-132012-06-132010Cohen, S.N. and Elliott, R.J., Comparisons for Backward Stochastic Differential Equations on Markov Chains and related No-Arbitrage Conditions, Annals of Applied Probability, January 2010, 20(1):267-3111050-5164http://hdl.handle.net/1880/48978Article deposited according to publisher policy posted on SHERPA/ROMEO, June 13, 2012Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Us- ing solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expec- tations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.engBackward stochastic differential equationMarkov chainsnon-linear expectationdynamic risk measurescomparison theoremjournal article10.11575/PRISM/34074