Comparison theorems for finite state backward stochastic differential equations
Date
2010
Authors
Cohen, S.
Elliott, R.
Editors
Chiarella, C.
Novikov, A.
Novikov, A.
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Book chapter
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Source details - Title: Contemporary quantitative finance: essays in honour of Eckhard Platen, 2010 / Chiarella, C., Novikov, A. (ed./s), Ch.8, pp.135-158
Statement of Responsibility
Samuel N. Cohen and Robert J. Elliott
Conference Name
International Conference on Quantitative Methods in Finance (2009 : Sydney, Australia)
Abstract
Most 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.
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© Springer-Verlag Berlin Heidelberg 2010