Differentiability of Quadratic BSDEs

  • Date: 03/21/2007

Gonçalo Jose Nunes dos Reis (Humboldt University Berlin)


University of British Columbia


We consider Backward Stochastic Differential Equations (BSDE) with
generators that grow quadratically in the control variable. In a more
abstract setting, we first allow both the terminal condition and the
generator to depend on a vector parameter $x$. We give sufficient
conditions for the solution pair of the BSDE to be differentiable in
$x$. This Parameter $x$ can be viewed as the initial condition of an
SDE, opening the way to differentiability of forward-backward systems.
Finally we 'prove' sufficient conditions for solutions of quadratic
BSDE to be differentiable in the variational sense (Malliavin
differentiable) and give representation formulas. These proofs are very
technical, so we will show simple sketches of them focusing on the
tools we used.


Probability Seminar 2007