Comparison Theorems for Finite State Backward Stochastic Differential Equations

Samuel N. Cohen () and Robert J. Elliott ()
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Samuel N. Cohen: University of Adelaide, School of Mathematical Sciences
Robert J. Elliott: University of Adelaide, School of Mathematical Sciences

A chapter in Contemporary Quantitative Finance, 2010, pp 135-158 from Springer

Abstract: Abstract Most previous contributions on BSDEs, and the related theories of non linear 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 discuss a theory of nonlinear expectations in the spirit of Peng ( math/0501415 (2005)). 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.

Keywords: Risk Measure; Stochastic Differential Equation; Terminal Condition; Comparison Theorem; Jump Time (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-03479-4_8

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DOI: 10.1007/978-3-642-03479-4_8

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