MT/15. Optional stopping theorem

The fifteenth video of the online series for Martingale Theory with Applications at the School of Mathematics, University of Bristol.

[@arianj2863]

Great video, thanks a lot!

[@vesperzhang6432]

So many thanks

[@ozgekaraoglan3359]

Heloo can I ask you what this theorem helps us do?

[@martonbalazsuob4363]

Good question as some of the practice problems we covered in class are not part of these publicly available lecture series. But Optional Stopping is among the few most used theorems in Martingales. One can use it to find expectations of stopping times or probabilities of reaching one state before another in certain scenarios. For two common applications search for 'ABRACADABRA' with martingales, or the gambler's ruin problem.

[@ozgekaraoglan3359]

@@martonbalazsuob4363 Thank you very much I've searched the ABRACADABRA application. Can I ask you if stopping times have anything common with Optimal Stopping Theory? I have a hard time aproaching this problem in a mathematical way.

[@martonbalazsuob4363]

@@ozgekaraoglan3359 I'm not sure I understand your question: this video is about the Optional Stopping Theorem in which stopping times play a fundamental role.

[@ozgekaraoglan3359]

@@martonbalazsuob4363 Well while I was researching it I came across antoher theory called the optimal stopping theory and wondered if they were similar but I understand better now