A numerical scheme for the quantile hedging problem
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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.
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