A numerical scheme for the quantile hedging problem
This work provides a convergent numerical scheme for quantile hedging, a problem relevant to financial practitioners dealing with market imperfections.
The authors propose a numerical method for quantile hedging in non-linear markets, proving convergence and demonstrating efficiency on a financial example with imperfections.
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.