Homeworks and final project done in the class "EDP en Finance" from M2MO (ex DEA Laure Elie) program at Université de Paris. All the code is done in Python.
The 1-st homework is about pricing european put options using implicit, explicit and Cranck-Nicolson schemes and then some basic analysis of the speed of convergence.
The 2-nd homework is about pricing american put options using splitting schemes (iplicit, explicit and Cranck-Nicolson), and then using different methods for the obstacle problem: PSOR, relaxed PSOR, Newton, Brennan and Schwartz and one higher order splitting scheme.
The final project ("Numerical methods for impulse control problem") is about stochastic optimal control, it is based on the chapter 7 of the paper C. Reisinger, Y. Zhang, "Error estimates of penalty schemes for quasi-variational inequalities arising from impulse control problems", arXiv:1901.07841v2.