​On May 29th, 2016, PhD Candidate Juho Häppölä presented his Proposal Thesis Defense entitled "Efficient computational methods for Stochastic Differential Equations"

We present past results and future prospects inefficient evaluation of payoff functionals on randomly evolving dynamic quantities. In the presentation, we go through recent results in Fourier methods for exponential levy processes and derive an adaptive multi-level time stepper for simulating SDEs. We also discuss on-going research on optimal stopping for stochastic differential equations.