Corpus ID: 231949227

Optimal stopping with signatures

@inproceedings{Bayer2020OptimalSW,
  title={Optimal stopping with signatures},
  author={C. Bayer and Paul Hager and Sebastian Riedel and J. Schoenmakers},
  year={2020}
}
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 X<∞ 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… Expand

References

SHOWING 1-10 OF 48 REFERENCES
Deep Optimal Stopping
TLDR
A deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples is developed, broadly applicable in situations where the underlying randomness can efficiently be simulated. Expand
FRACTIONAL BROWNIAN MOTION WITH HURST INDEX H=0 AND THE GAUSSIAN UNITARY ENSEMBLE
The goal of this paper is to establish a relation between characteristic polynomials of N×N GUE random matrices H as N→∞, and Gaussian processes with logarithmic correlations. We introduce aExpand
Monte Carlo Valuation of American Options
This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of theExpand
Log-Modulated Rough Stochastic Volatility Models
We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernelExpand
Optimal Execution with Rough Path Signatures
TLDR
Following an approximation of the optimisation problem, this work is able to calculate an optimal solution for the trading speed in the space of linear functions on a truncation of the signature of the price process. Expand
Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close toExpand
Functional Itô Calculus
Ito calculus deals with functions of the current state whilst we deal with functions of the current path to acknowledge the fact that often the impact of randomness is cumulative. We express theExpand
A Course on Rough Paths: With an Introduction to Regularity Structures
Introduction.- The space of rough paths.- Brownian motion as a rough path.- Integration against rough paths.- Stochastic integration and Ito's formula.- Doob-Meyer type decomposition for roughExpand
Uniqueness for the signature of a path of bounded variation and the reduced path group
We introduce the notions of tree-like path and tree-like equivalence between paths and prove that the latter is an equivalence relation for paths of finite length. We show that the equivalenceExpand
A regularity structure for rough volatility
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructureExpand
...
1
2
3
4
5
...