Optional stopping theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 28/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Optional_stopping_theorem


00:00:55 1 Statement of theorem
00:03:29 1.1 Remark
00:03:41 2 Applications
00:03:57 3 Proof
00:04:06 4 References
00:06:09 5 External links
00:06:37 Xn2 – n martingale from the examples section. If τ is the time at which X first reaches ±m, then 0
00:06:51 E[Yτ]
00:07:40 0. The failure of the optional stopping theorem shows that all three of the conditions fail.
00:07:50 Proof



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SUMMARY
=======
In probability theory, the optional stopping theorem (or Doob's optional sampling theorem) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. Since martingales can be used to model the wealth of a gambler participating in a fair game, the optional stopping theorem says that, on average, nothing can be gained by stopping play based on the information obtainable so far (i.e., without looking into the future). Certain conditions are necessary for this result to hold true. In particular, the theorem applies to doubling strategies.
The optional stopping theorem is an important tool of mathematical finance in the context of the fundamental theorem of asset pricing.