I will cover regular and singular perturbations methods for linear and nonlinear problems arising in financial mathematics. Pricing and hedging options in the context of mult-timescale stochastic volatility gives rise to linear problems, and portfolio optimization are typically described by nonlinear problems.

**Prerequisites:** Being familiar with pricing and hedging financial derivatives and their associated linear PDEs, portfolio optimization and associated HJB equations, and stochastic volatility modeling. In other words, PSTAT 223 A and B (or equivalent). However, I will recall the main ingredients as we go.

fouque at pstat.ucsb.edu## Office: South Hall 5504

Jean-Pierre Fouque