Course starts on the week of April 19th and will meet weekly on Wednesdays from 9:30 to 12:15 and then again from 1:30 to 4:15 for about 6.5 weeks until roughly the 1st week of June.

Please note that class on Wednesday May 19 will be meeting in the 3rd Floor Stewart Library.

The last class on May 26 has been rescheduled to Tuesday June 8 in the 3rd Floor Stewart Library

Lecture Notes

I- Stochastic control and viscosity solutions

1- Formulation
2- Dynamic Programming principle
3- Verification, application to finance
4- Introduction to viscosity solutions of second order PDEs
5- Stochastic control and viscosity solutions
6- Applications: hedging under portfolio constrants

II- Backward stochastic differential equations

1- Existence and uniqueness
2- The Markov case
3- Connection with semilinear PDEs
4- Applications: interacting optimal investors with performance concern

III- Probabillistic numerical methods for nonlinear PDEs

1- Introduction to Monte Carlo methods
2- Probabillistic algorithms for American options
3- Numerical scheme for fully nonlinear PDEs
4- Convergence
5- Bounds on the rate of convergence

IV- Introduction to Second order backward SDEs

1- G-expectation, application to finance
2- Second order target problems, application to finance
3- Second order BSDEs

Guest lectures:

It is a great pleasure to have Bruno Bouchard (University Paris Dauphine), Mete Soner (ETH Zurich), and Agnès Tourin (Fields Research Immersion Fellow), giving advanced lectures as an integral part of the course. Bruno will be giving the afternoon sessions of the 5th and the 12th of May.
Mete will be giving the morning session of June 2.
Agnès will be giving the afternoon session of June 2. (Lecture Notes)