Abstract
Optimal stopping rules are developed to maximize a reward or minimize a loss in a martingale framework by stopping the process at the right time. Applications include the pricing of American options and the “search for the best” (secretary problem) algorithm.
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Notes
- 1.
The secretary problem has an interesting history recorded by Ferguson (1989), with numerous references. There is also a rather large literature on generalizations to lower order preferences than the best, e.g., search for second best, to partially ordered preferences, and so-on of interest in theories and models for ecological foraging, on-line marketing, and others.
References
Ferguson T (1989) Who solved the secretary problem? Statist Sci 4(3):282–289.
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Bhattacharya, R., Waymire, E.C. (2021). Special Topic: Optimal Stopping Rules. In: Random Walk, Brownian Motion, and Martingales. Graduate Texts in Mathematics, vol 292. Springer, Cham. https://doi.org/10.1007/978-3-030-78939-8_24
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