On the orthogonal component of BSDEs in a Markovian setting

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.

Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions

Two discretizations of a novel class of Markovian backward stochastic differential equations (BSDEs) are studied. The first is the classical Euler scheme which approximates a projection of the processes Z, and the second a novel scheme based on Malliavin weights which approximates the mariginals of the process Z directly. Extending the representation theorem of Ma and Zhang [MZ02] leads to adva...

N ov 2 01 6 Solving Backward Stochastic Differential Equations by Connecting the Short - term Expansions ∗

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expec...

Numerical simulation of quadratic BSDEs

This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to z and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we ...

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition