Economics, Finance, Business and Management 2 A change-of-variable formula with local time on surfaces 1 American option 1 American options 1 Brownian motion 1 Calibration 1 De-Americanization 1 Filtering estimate 1 Free-boundary problem 1 Heston model 1 Hidden markov chain 1 Innovation process 1 Model reduction 1 Monte Carlo 1 Optimal stopping problem 1 Perpetual American options 1 Random dividends 1 Reduced basis method (RBM) 1 deep learning 1 optimal stopping 1 reinforcement learning 1