A book project by José Correa, Paul Dütting, Michal Feldman, Thomas Kesselheim, and Brendan Lucier.

The Prophet Inequality is a classic and beautiful mathematical result from the 70s. This tool for stochastic optimization has seen a resurgence in popularity in the last decade due to its relevance in a variety of important applications, such as ad auctions and ride sharing. This recent excitement has led to an explosive growth of new theory and variations on the classic Prophet inequality.

In this book we provide a comprehensive overview of the rich new theory that has been developed over the past decade. This comprises techniques such as balanced prices and online contention resolution schemes, along with data-driven approaches.

Preliminary Version of Chapters 1 to 4 (PDF)

This is an early draft. Comments are welcome.

This material will be published by Cambridge University Press as Prophet Inequalities: Theory and Methods by José Correa, Paul Dütting, Michal Feldman, Thomas Kesselheim, and Brendan Lucier. This pre-publication version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © copyright by J. Correa, P. Dütting, M. Feldman, T. Kesselheim, and B. Lucier, 2025