The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 20, Number 1 (2010), 267-311.
Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
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.
Ann. Appl. Probab., Volume 20, Number 1 (2010), 267-311.
First available in Project Euclid: 8 January 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 91B70: Stochastic models
Cohen, Samuel N.; Elliott, Robert J. Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions. Ann. Appl. Probab. 20 (2010), no. 1, 267--311. doi:10.1214/09-AAP619. https://projecteuclid.org/euclid.aoap/1262962324