Optimal stopping with signatures
By Christian Bayer, Paul Hager, Sebastian Riedel, John Schoenmakers. The Annals of Applied Probability, 2021
49 citations recorded by the source corpus.
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 $\mathbb{X}^{<\infty}$ 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 $\mathbb{E}\left[ \mathbb{X}^{\le N}_{0,T} \right]$. 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. on financial or electricity markets.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/88d34f55301dbface82df2d7c7cda498b2e95314
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Citations in the corpus
- Joint calibration to SPX and VIX options with signature‐based models (2023, background): “This is similar as in Cuchiero et al. (2022a) or Bayer et al. (2021), but to keep the paper self-contained we recall the essential definitions and properties.”