【好帖重赏】对鞅的理解

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下面是鞅的有关定义，将它用于资产定价时，应该如何理解其背后的经济学含义？
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关键词：如何理解 资产定价 经济学 论坛币 如何 经济学

转自玄霄版主：
鞅是随机过程的一种，它的显著特点是未来的期望等于现在。一个随机过程一般伴随着一个测度。测度是满足一定条件的取值为非负的集函数，两个测度等价是指这两个函数具有相同的支撑，支撑是指使函数值大于零的定义域。
    等价鞅测度即是把不是鞅的随机过程转化成鞅的测度。这一测试和原来随机过程伴随的测试等价。转化成鞅后，可是直接采用求数学期望的方法来获得金融衍生产品的价格，如期权，而不用解偏微分方程了。也不知说清楚了没有，可以参见 John Hull 的书。

本文来自: 人大经济论坛 金融工程（数量金融）与金融衍生品 版，详细出处参考： https://bbs.pinggu.org/forum.php?mod=viewthread&tid=1013520&page=1&from^^uid=2789966

我们这里的上鞅，以及半鞅和局部鞅。这三者之间有没有关系？

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表现了人类权衡风险和收益的一种本能，martingale要求未来的条件期望等于现在的状态，是“中庸”地展望未来，也许是若干年进化形成的心理。

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

谢谢，敢问您这里的“中庸”是否为风险中性的同义转述？

chengzhifu2013 发表于 2015-4-14 18:19
谢谢，敢问您这里的“中庸”是否为风险中性的同义转述？

希望不可知的未来平均来看是中庸的，可以看做是从人性层面上理解“风险中性”

自己顶

半鞅分为上鞅和下鞅，都属于局部鞅

建议看看随机过程