Abstract
Abstract The Skorokhod embedding problem, in its essence, amounts to designing a stopping time such that, at that time, a given stochastic process has a prescribed distribution. It has been an active field of research in probability for over 40 years now. We discuss some of the key results in the domain, along with their applications in financial mathematics, namely, in robust pricing and hedging of exotic derivatives. More precisely, we establish a correspondence between solutions to the Skorokhod embedding problem and possible market models matching given prices of vanilla options for a fixed maturity. No‐arbitrage bounds on a price of an exotic derivative are then obtained through an optimization over solutions to the embedding problem. Pathwise understanding of the embedding often allows us to derive the associated robust (often model‐free) superhedges. We illustrate these techniques with an example of a one‐touch option. No‐arbitrage bounds on its price are induced by the Azéma–Yor and Perkins solutions to the Skorokhod embedding; the associated superhedging strategy was deduced by Hobson.
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