On Markovian solutions to Markov Chain BSDEs

Undiscounted Markov Chain BSDEs to Stopping Times

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...

A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition

In [17], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that the existence result remains true for these BSDEs when the regularity assumptions on the terminal condition is weakened.

On the orthogonal component of BSDEs in a Markovian setting

Abstract In this Note we consider a quadratic backward stochastic differential equation (BSDE) driven by a continuous martingale M and whose generator is a deterministic function. We prove (in Theorem 2.1) that if M is a strong homogeneous Markov process and if the BSDE has the form (1.2) then the unique solution (Y, Z,N) of the BSDE is reduced to (Y, Z), i.e. the orthogonal martingale N is equ...

Ergodic BSDEs Driven by Markov Chains

We consider ergodic backward stochastic differential equations, in a setting where noise is generated by a countable state uniformly ergodic Markov chain. We show that for Lipschitz drivers such that a comparison theorem holds, these equations admit unique solutions. To obtain this result, we show by coupling and splitting techniques that uniform ergodicity estimates of Markov chains are robust...

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition