Undiscounted Markov Chain BSDEs to Stopping Times. (30th January 2018)

• Record Type: Journal Article
• Authors: Cohen, Samuel N.
• Is Part Of: Journal of applied probability. Volume 51:Number 1(2014)
• Page Start: 262
• Page End: 281
• Publication Date: 2018-01-30
• Subjects: BSDE, -- Markov chain, -- uniform ergodicity, -- risk averse control, -- non-Ohmic circuit; 60J27, -- 93E20, -- 94C05; 519.2
• DOI: 10.1239/jap/1395771428
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : We consider backward stochastic differential equations in a setting where noise is generated by a countable state, continuous time Markov chain, and the terminal value is prescribed at a stopping time. We show that, given sufficient integrability of the stopping time and a growth bound on the terminal value and BSDE driver, these equations admit unique solutions satisfying the same growth bound (up to multiplication by a constant). This holds without assuming that the driver is monotone in y, that is, our results do not require that the terminal value be discounted at some uniform rate. We show that the conditions are satisfied for hitting times of states of the chain, and hence present some novel applications of the theory of these BSDEs.