COMPARISONS FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MARKOV CHAINS AND RELATED NO-ARBITRAGE CONDITIONS
成果类型：
Article
署名作者：
Cohen, Samuel N.; Elliott, Robert J.
署名单位：
University of Adelaide; University of Calgary
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/09-AAP619
发表日期：
2010
页码：
267-311
关键词：
摘要：
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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