Cohen, S.Elliott, R.Chiarella, C.Novikov, A.2011-06-242011-06-242010Source details - Title: Contemporary quantitative finance: essays in honour of Eckhard Platen, 2010 / Chiarella, C., Novikov, A. (ed./s), Ch.8, pp.135-1589783642034787http://hdl.handle.net/2440/64824Most previous contributions on BSDEs, and the related theories of non linear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov Chains, we discuss a theory of nonlinear expectations in the spirit of Peng (math/0501415 (2005)). 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.en© Springer-Verlag Berlin Heidelberg 2010BSDEMarkov chainarbitragerisk measuresnon-linear expectationsBook chapter002010130510.1007/978-3-642-03479-4_800028352970000833018