Journal
ANNALS OF APPLIED PROBABILITY
Volume 20, Issue 1, Pages 267-311Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/09-AAP619
Keywords
Backward stochastic differential equation; Markov chains; nonlinear expectation; dynamic risk measures; comparison theorem
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Funding
- SSHRC
- Australian Research Council
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Most 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. Using 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 expectations (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.
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