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Type: Journal article
Title: Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
Author: Cohen, S.
Elliott, R.
Citation: Annals of Applied Probability, 2010; 20(1):267-311
Publisher: Inst Mathematical Statistics
Issue Date: 2010
ISSN: 1050-5164
Statement of
Samuel N. Cohen and Robert J. Elliott
Abstract: 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.
Keywords: Backward stochastic differential equation
Markov chains
nonlinear expectation
dynamic risk measures
comparison theorem
Rights: © Institute of Mathematical Statistics, 2010
DOI: 10.1214/09-AAP619
Grant ID: ARC
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