# Non linear pricing

Julien Guyon

The idea of the course is to present a broad spectrum of mathematical tools (in Analysis, Probability, Geometry, Optimization) to solve concrete problems in quantitative finance.

During each session, a concrete problem associated with a mathematical tool will be presented. Here are some examples:

- Calibration of stochastic volatility models and nonlinear McKean equation.
- Uncertain volatility model and backward stochastic equations.
- Counterparty risk and branching processes.
- Exotic hedging doptions by vanillas and martingale optimal transport.
- Non-arbitrable parametric smiles and hyperbolic geometry.

## References

- Henry-Labordère, P. : Analysis, Geometry and Modeling in Finance: Advanced Methods in Option Pricing, Financial Mathematics Series CRC, Chapman Hall.
- Guyon, J., Henry-Labordère, P. : Nonlinear option pricing, Financial Mathematics Series CRC, Chapman Hall.
- Henry-Labordère, P. : Optimal transport, geometry and Monte-Carlo methods for nonlinear PDEs: A ride in mathematical finance, https://hal.archives-ouvertes.fr/tel-01088419/document