Nicole El Karoui delivered the Coxeter Lectures Series for our thematic program this week. The theme of the lectures were backward stochastic differential equations (BSDEs), a vast and deep topic to which she has made groundbreaking contributions over the past couple couple of decades.
The first lecture was an overview of the main definitions, results and classical applications to finance, along the lines of her well-known 1997 paper with Peng and Quenez. It went about half an hour overtime, but she is so passionate about the subject that nobody minded much.
I could not attend the second lecture (was organizing a "help your child with math" event at my son's school the same evening), but was told by other participants that it covered the more mathematical aspects of the theory, showing what goes under the hood when one tries to prove things like existence, uniqueness and stability of solutions of BSDEs.
In the third and final lecture, Nicole concluded a discussion of numerical schemes for approximating solutions of BSDEs by showing what kind of errors need to be controlled, together with a few convergence results. She then switched gears to finance again and described how certain BSDEs can be viewed as dynamic risk measures - a challenging new focus of intense research in the area.