Talk

Optimal stopping with signatures

13.06.2022 16:45 - 17:45

 

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 X.
We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature Chi<∞ associated to X, 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 process X 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. of financial or electricity markets.

Based on joint work with Paul Hager, Sebastian Riedel, and John Schoenmakers

Underlying paper: https://arxiv.org/abs/2105.00778

Personal website of Christian Bayer

 

The talk also can be joined online via our ZOOM MEETING

Meeting room opens at: June 13, 2022, 4.30 pm Vienna

Meeting ID: 612 3972 5358

Password: 453166

 

 

 

Location:
HS 7 OMP1 (#1.303)