COMPARISONS FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MARKOV CHAINS AND RELATED NO-ARBITRAGE CONDITIONS
Date
2010
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Matehmatical Statistics
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. Us-
ing 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 expec-
tations (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.
Description
Article deposited according to publisher policy posted on SHERPA/ROMEO, June 13, 2012
Keywords
Backward stochastic differential equation, Markov chains
Citation
Cohen, S.N. and Elliott, R.J., Comparisons for Backward Stochastic Differential Equations on Markov Chains and related No-Arbitrage Conditions, Annals of Applied Probability, January 2010, 20(1):267-311