In this project, our interest is to develop numerical scheme for a class of BSDEs with weak terminal condition. This class of BSDEs was introduced by Bouchard, Elie and Reveillac [1], in which the terminal value YT of the portfolio is required to satisfy a weak constraint. From a financial point of view, this approach is referred to as quantile or efficient hedging, and was first discussed by F ̈ollmer and Leukert [2, 3]. In particular, they explained how the so-called quantile hedging price for European option can be computed explicitly in a complete market, using duality arguments and Neyman-Pearson lemma.

References [1] Bruno Bouchard, Romuald Elie, and Antony Rveillac. Bsdes with weak terminal con- dition. The Annals of Probability, 43(2):572–604, 2015.

[2] Hans F ̈ollmer and Peter Leukert. Quantile hedging. Finance Stoch., 3(3):251–273, 1999.

[3] Hans F ̈ollmer and Peter Leukert. Efficient hedging: cost versus shortfall risk. Finance Stoch., 4(2):117–146, 2000.