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Type: Journal article
Title: Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise
Author: Yang, Z.
Ramarimbahoaka, D.
Elliott, R.
Citation: Electronic Communications in Probability, 2016; 21(none):25-1-25-10
Publisher: Institute of Mathematical Statistics (IMS) and the Bernoulli Society
Issue Date: 2016
ISSN: 1083-589X
Statement of
Zhe Yang, Dimbinirina Ramarimbahoaka, Robert J. Elliott
Abstract: Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with Markov chain noise, adapting previous results under simplified hypotheses. We introduce a type of nonlinear expectation, the f-expectation, which is an interpretation of the solution to a BSDE, and use it to establish a converse comparison theorem for the same type of equations as those in the comparison results.
Keywords: BSDEs; comparison theorem; converse comparison; Markov chain
Rights: Creative Commons Attribution License. Attribution 4.0
RMID: 0030047440
DOI: 10.1214/16-ECP4102
Appears in Collections:Mathematical Sciences publications

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