Stochastics and Finance: Kihun Nam -- Global Well-posedness of non-Markovian multidimensional superquadratic BSDEs

Speaker: Dr Kihun Nam (Monash University) 

Title: Global Well-posedness of non-Markovian multidimensional superquadratic BSDEs 

Using a purely probabilistic argument, we prove the global well-posedness of
multidimensional superquadratic backward stochastic differential equations (BSDEs)
without Markovian assumption.  The key technique is the interplay between the local
well-posedness of fully coupled path-dependent forward backward stochastic differential
equations (FBSDEs) and backward iterations of the superquadratic BSDE.  The
superquadratic BSDE studied in this article includes quadratic BSDEs appear in
stochastic differential game and price impact model.  We also study the well-posedness
of superquadratic FBSDE using the corresponding BSDE results.  Our result also provides
the well-posedness of a system of path-dependent quasilinear partial differential
equations where the nonlinearity has superquadratic growth in the gradient of the
solution.

http://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html