Martingales
Research output: Contribution to book/conference proceedings/anthology/report › Chapter in book/anthology/report › Contributed › peer-review
Contributors
Abstract
A martingale is the mathematical description of a fair game: The expected net gain or loss from further play, independent of the history, is 0. The rigorous mathematical definition involves conditional expectation. Following earlier work by Paul Lévy and Jean Ville, Joseph Leo Doob developed in the 1940s and 1950s basic martingale theory and many of its applications. Martingales allowed one to study, for the first time, the behavior of sums and sequences of random variables which are not independent. Martingale theory is one of the cornerstones of modern mathematical probability theory with wide-ranging applications in stochastic analysis and mathematical finance.
Details
| Original language | English |
|---|---|
| Title of host publication | International Encyclopedia of the Social & Behavioral Sciences: Second Edition |
| Publisher | Elsevier Inc. |
| Pages | 630-634 |
| Number of pages | 5 |
| ISBN (electronic) | 9780080970875 |
| ISBN (print) | 9780080970868 |
| Publication status | Published - 26 Mar 2015 |
| Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- Banach-space geometry, Berry-Esseen theorem, Central limit theorem, Conditional probability, Fair game, Gambling strategy, Game theory, Harmonic analysis, Likelihood ratio, Martingale, Mathematical finance, Optimal stopping, Stochastic (Itô) integral, Stochastic analysis, Stochastic process