9th European Summer School in Financial Mathematics Pushkin, St. Petersburg, 29 August - 2 September 2016

Grand Cascade in Petrodvorets. Photo: A.Savin, Wikimedia Commons

Main Lecture Courses

The summer school will be structured around two main topics:

  • Numerical methods for nonlinear problems. Minicourses will be given by Bruno Bouchard (Paris-Dauphine Univesity) and Nizar Touzi (Ecole Polytechnique)
  • Financial markets with arbitrage. Minicourses will be given by Kostas Kardaras (London School of Economics) and Johannes Ruf (University College London).
  • In addition, a minicourse on performance measures will be given by Mikhail Zhitlukhin (Steklov mathematical institute).

Market viability and hedging beyond NFLVR
Kostas Kardaras (London School of Economics)

  • Fundamental Theorems under a weaker market viability condition than No Free Lunch with Vanishing Risk (NFLVR).
  • Hedging duality and its applications.
  • Extensions to infinite-asset market models.


Arbitrage opportunities relative to the market
Johannes Ruf (University College London)

  • Introduction to stochastic portfolio theory
  • The theory of functionally generated trading strategies
  • Suitable conditions guaranteeing that these trading strategies almost surely outperform the market
  • The question of the existence of short-term arbitrage in market models


Monte-Carlo approximations of backward stochastic differential equations
Bruno Bouchard (Paris Dauphine University)

We will study Monte-Carlo approximations of backward stochastic differential equations (BSDEs), which provide a numerical tool for the resolution of semi-linear parabolic partial differential equations (PDEs). We shall first briefly review the links between BSDEs and PDEs and then discuss the (abstract) Euler-type discrete time approximation of BSDEs (standard, reflected, with Dirichlet type boundary condition, with irregular terminal condition). The later involves the computation of conditional expectations. Two techniques will be considered. One consists in using the Malliavin calculus to rewrite condition expectations as the ratio of two unconditional ones, the second uses non-parametric regression techniques.


Branching particle representations of solutions to partial differential equations
Nizar Touzi (Ecole Polytechnique)

We provide a representation of the solution of a semilinear partial differential equation by means of a branching diffusion. Unlike the backward SDE approach, such a representation induces a purely forward Monte Carlo method. We also provide applications to the unbiased simulation of stochastic differential equations.


Performance measures: axiomatics and concrete examples
Mikhail Zhitlukhin (Steklov Mathematical Institute, Moscow)

I will give a brief overview of the theory of performance measures, which is an approach to evaluate investment strategies based on ideas similar to convex and coherent risk measures. We will start with abstract axiomatics, prove a representation theorem, and then look at specific examples and discuss numerical implementations.


Contact: summerschoolmathfi@mi.ras.ru or summerschoolmathfi@cmap.polytechnique.fr