  We consider the numerical approximation of the quantile hedging price in a
non-linear market. In a Markovian framework, we propose a numerical method
based on a Piecewise Constant Policy Timestepping (PCPT) scheme coupled with a
monotone finite difference approximation. We prove the convergence of our
algorithm combining BSDE arguments with the Barles & Jakobsen and Barles &
Souganidis approaches for non-linear equations. In a numerical section, we
illustrate the efficiency of our scheme by considering a financial example in a
market with imperfections.
