The Annals of Applied Probability

Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions

Samuel N. Cohen and Robert J. Elliott

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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.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 1 (2010), 267-311.

Dates
First available in Project Euclid: 8 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1262962324

Digital Object Identifier
doi:10.1214/09-AAP619

Mathematical Reviews number (MathSciNet)
MR2582649

Zentralblatt MATH identifier
1195.60077

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 91B70: Stochastic models

Keywords
Backward stochastic differential equation Markov chains nonlinear expectation dynamic risk measures comparison theorem

Citation

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


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