Optimal Stopping for Non-Markovian Asset Price Processes

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Abstract
Some of the most liquidly traded options in equity markets are American and Bermudan options, whose owner may choose the option’s exercise date—within a certain range. Hence, these options are optimal stopping problems from a mathematical perspective. There is a huge literature on solving optimal stopping problems, and most of the prevalent methods (e.g., solving the Hamilton-Jacobi-Bellman PDE, least squares Monte Carlo, dual martingale methods) strongly rely on the Markov property for the underlying dynamics, to avoid the curse of dimensionality. In this chapter, we will show how the signature can be used to adopt classical, Markovian numerical methods for the non-Markovian case.