P. Hager (Technische Universität Berlin)
Tuesday, May 11, 2021 - 15:00
Online Event
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715, --- ---
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature associated to the underlying process, and prove that maximizing over these classes of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature. By applying a deep neural network approach to approximate the non-linear signature functionals, we can efficiently solve the optimal stopping problem numerically. The only assumption on the underlying process is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion, which fail to be either semi-martingales or Markov processes, and can be used, in particular, for American-type option pricing in fractional models, e.g. on financial or electricity markets. This is a joint work with Christian Bayer, Sebastian Riedel and John Schoenmakers.
submitted by chschnei (christine.schneider@wias-berlin.de, 030 20372574)