### Machine Learning with Financial Applications

The lecture covers the following topics:

**Statistical learning, neural networks, and deep model calibration**

Polynomial curve fitting, foundations of statistical learning, no free lunch theorem, local volatility, interpolation of volatility surfaces, universal approximation, approximation by deep neural networks, empirical risk minimization, ridge regression, nonlinear regression, convex optimization, gradient descent, stochastic gradient descent, non-convex optimization, calibration of financial models, machine learning techniques for option pricing, deep model calibration.

**Backward SDEs and deep solvers for PDEs**

BSDE approach to option pricing, deep solvers for BSDEs, Euler-Maruyama discretization of forward SDEs, existence and uniqueness of backward SDEs, linear BSDEs, applications in option pricing, comparison principles, Euler-Maruyama discretization of backward SDEs, classical solutions of semilinear PDEs, convergence rates of deep solvers for backward SDEs, scope and limitations.

**Optimal stopping and American options**

Discrete time optimal stopping, Snell envelope, optimal stopping times, American put option, martingale duality, parametric approximation methods, regression based approximation methods, Longstaff-Schwartz algorithm, martingales from stopping rules, deep optimal stopping, low rank tensors, signatures and rough paths, optimal stopping with signatures.

**Markov decision processes and reinforcement learning**

Optimal liquidation problems, Markov decision processes, dynamic programming, Bellman equation, tabular methods, Q-learning, Monte Carlo methods, temporal difference methods, optimal liquidation revisited, optimal investment, deep Q-learning.