Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
By Samuel N. Cohen, Robert J. R. Elliott. 2008
87 citations recorded by the source corpus.
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.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/97f79deb663e23bf5160e7569651fe6db7f975ee
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In Finance
- Samuel N. Cohen
- Robert J. R. Elliott
- Tomasz Klimsiak
- Tak Kuen Siu
- Guang-Hua Lian
- Alessandro Ramponi
- Leunglung Chan
- David Nualart
In Management Science and Operations Research
Citations in the corpus
- Existence and Comparisons for BSDEs in general spaces (2010, methodology): “When the filtration is generated by a Poisson random measure over a separable space and a Brownian motion, as in [2, 22] and others, or by a Markov chain, as in [4, 5], we have a similar reduction.”