翻訳と辞書 Words near each other ・ Option Zero ・ Option-adjusted spread ・ Option-operand separation ・ Optional federal charter ・ Optional flex acreage ・ Optional Practical Training ・ Optional preferential voting ・ Optional Protocol on the Involvement of Children in Armed Conflict ・ Optional Protocol on the Sale of Children, Child Prostitution and Child Pornography ・ Optional Protocol to the Convention against Torture ・ Optional Protocol to the Convention on the Elimination of All Forms of Discrimination against Women ・ Optional Protocol to the Convention on the Rights of Persons with Disabilities ・ Optional Protocol to the Convention on the Rights of the Child on a Communications Procedure ・ Optional Protocol to the International Covenant on Economic, Social and Cultural Rights ・ Optional referendum ・ Optional stopping theorem ・ Optionally piloted vehicle ・ Options (novel) ・ Options arbitrage ・ Options backdating ・ Options broker ・ Options Clearing Corporation ・ Options counseling ・ Options for Change ・ Options Market France ・ Options of a Trapped Mind ・ Options Price Reporting Authority ・ Options Secondary School ・ Options spread ・ Options strategies Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Optional stopping theorem ： ウィキペディア英語版 Optional stopping theorem In probability theory, 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 the expected value of its initial 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 the average nothing can be gained by stopping to play the game based on the information obtainable so far (i.e., by not looking into the future). Of course, certain conditions are necessary for this result to hold true, in particular doubling strategies have to be excluded. The optional stopping theorem is an important tool of mathematical finance in the context of the fundamental theorem of asset pricing. == Statement of theorem == A discrete-time version of the theorem is given below: Let be a discrete-time martingale and a stopping time with values in }, both with respect to a filtration . Assume that one of the following three conditions holds: :() The stopping time is almost surely bounded, i.e., there exists a constant such that a.s. :() The stopping time has finite expectation and the conditional expectations of the absolute value of the martingale increments are almost surely bounded, more precisely, and there exists a constant such that Then is an almost surely well defined random variable and $\backslash mathbb()=\backslash mathbb().$ Similarly, if the stochastic process is a submartingale or a supermartingale and one of the above conditions holds, then :$\backslash mathbb()\backslash ge\backslash mathbb(),$ for a submartingale, and :$\backslash mathbb()\backslash le\backslash mathbb(),$ for a supermartingale. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Optional stopping theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.