【好帖重賞】對鞅的理解

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下面是鞅的有關(guān)定義，將它用于資產(chǎn)定價(jià)時(shí)，應(yīng)該如何理解其背后的經(jīng)濟(jì)學(xué)含義？
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關(guān)鍵詞：如何理解 資產(chǎn)定價(jià) 經(jīng)濟(jì)學(xué) 論壇幣 如何 經(jīng)濟(jì)學(xué)

轉(zhuǎn)自玄霄版主：
鞅是隨機(jī)過程的一種，它的顯著特點(diǎn)是未來的期望等于現(xiàn)在。一個(gè)隨機(jī)過程一般伴隨著一個(gè)測度。測度是滿足一定條件的取值為非負(fù)的集函數(shù)，兩個(gè)測度等價(jià)是指這兩個(gè)函數(shù)具有相同的支撐，支撐是指使函數(shù)值大于零的定義域。
    等價(jià)鞅測度即是把不是鞅的隨機(jī)過程轉(zhuǎn)化成鞅的測度。這一測試和原來隨機(jī)過程伴隨的測試等價(jià)。轉(zhuǎn)化成鞅后，可是直接采用求數(shù)學(xué)期望的方法來獲得金融衍生產(chǎn)品的價(jià)格，如期權(quán)，而不用解偏微分方程了。也不知說清楚了沒有，可以參見 John Hull 的書。

本文來自: 人大經(jīng)濟(jì)論壇 金融工程（數(shù)量金融）與金融衍生品 版，詳細(xì)出處參考： http://xalimeijing.com/forum.php?mod=viewthread&tid=1013520&page=1&from^^uid=2789966

我們這里的上鞅，以及半鞅和局部鞅。這三者之間有沒有關(guān)系？

摘自wiki：
Originally, martingale referred to a class of betting strategies that was popular in 18th-century France.[1][2] The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake. As the gambler's wealth and available time jointly approach infinity, his probability of eventually flipping heads approaches 1, which makes the martingale betting strategy seem like a sure thing. However, the exponential growth of the bets eventually bankrupts its users, assuming the obvious and realistic i.e. finite bankrolls (one of the reasons casinos, though normatively enjoying a mathematical edge in the games offered to their patrons, impose betting limits). Stopped Brownian motion, which is a martingale process, can be used to model the trajectory of such games.

martingale表現(xiàn)了人類權(quán)衡風(fēng)險(xiǎn)和收益的一種本能，martingale要求未來的條件期望等于現(xiàn)在的狀態(tài)，是“中庸”地展望未來，也許是若干年進(jìn)化形成的心理。

xuruilong100 發(fā)表于 2015-4-14 18:03
摘自wiki：
Originally, martingale referred to a class of betting strategies that was popular in 18t ...

謝謝，敢問您這里的“中庸”是否為風(fēng)險(xiǎn)中性的同義轉(zhuǎn)述？

chengzhifu2013 發(fā)表于 2015-4-14 18:19
謝謝，敢問您這里的“中庸”是否為風(fēng)險(xiǎn)中性的同義轉(zhuǎn)述？

希望不可知的未來平均來看是中庸的，可以看做是從人性層面上理解“風(fēng)險(xiǎn)中性”

自己頂

半鞅分為上鞅和下鞅，都屬于局部鞅

建議看看隨機(jī)過程