PDE Seminar Abstracts

Option pricing with market impact and non-linear Black and Scholes equations

Grégoire Loeper
Monash University
Mon 9th May 2016, 2-3pm, Carslaw Room 829 (AGR)


We will introduce a model of option pricing with market impact, where the option’s seller modifies the underlying’s volatility through the dynamic delta-hedging. The pricing equation becomes then a fully non-linear singular parabolic equation, and I will expose some results obtained on this equation.

This problem belongs to the class of so-called second order stochastic target problems studied by Soner and Touzi, and I will also spend some time giving a brief overview of this topic, and its links with optimal transportation and fully non-linear parabolic equations