请问什么是martingale property????

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看书的时候碰到了这个词，实在不明白到底是什么样一个instrument?在网上搜索也很少能搜到相关解释！help！先谢过拉~~~~~~

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关键词：Martingale property Martin artin Mart property Martingale

Let (Omega, F, P) be a probability space, let T be a fixed positive number, and let F(t), 0 <= t <= T, be a filtration of sub-sigma-algebras of F. Consider an adapted stochastic process M(t), 0 <= t <= T. If E[M(t)|F(s)] = M(s) for all 0 <= s <= t <= T, we say this process is a martingale. It has no tendency to rise or fall.

是不是说了等于没说一样？

[此贴子已经被作者于2007-2-6 9:56:40编辑过]

以下是引用irvingy在2007-2-6 9:56:00的发言：

Let (Omega, F, P) be a probability space, let T be a fixed positive number, and let F(t), 0 <= t <= T, be a filtration of sub-sigma-algebras of F. Consider an adapted stochastic process M(t), 0 <= t <= T. If E[M(t)|F(s)] = M(s) for all 0 <= s <= t <= T, we say this process is a martingale. It has no tendency to rise or fall.

是不是说了等于没说一样？

这个解释太数学化了，hehe,

还是找本概率论的书看看吧，一般都有martingale的初步介绍。

他的中文解释是什么呢?

呵呵,其实主要的就是这个式子

E[M(t)|F(s)] = M(s) for all 0 <= s <= t <= T

以下是引用垃圾树在2007-2-6 19:18:00的发言：

呵呵,其实主要的就是这个式子

E[M(t)|F(s)] = M(s) for all 0 <= s <= t <= T

的确，数学上主要是这个式子，但金融学上的应用有没？给个例子？

印象中以前有遇到过这个词，但一下子记不清了。。。

[此贴子已经被作者于2007-2-6 21:57:14编辑过]

以下是引用skywater83在2007-2-6 21:52:00的发言：

的确，数学上主要是这个式子，但金融学上的应用有没？给个例子？

印象中以前有遇到过这个词，但一下子记不清了。。。

金融上的应用就是寻找一个合适的概率空间(一般来说就是不同的贴现率),使得某个随机过程(如衍生品价格)是一个鞅,那么定价就容易多了.

PS:下学期会讲到的哈

以下是引用垃圾树在2007-2-6 22:19:00的发言：

金融上的应用就是寻找一个合适的概率空间(一般来说就是不同的贴现率),使得某个随机过程(如衍生品价格)是一个鞅,那么定价就容易多了.

PS:下学期会讲到的哈

眨啥眼睛。。。恶心。。。呵呵

“寻找一个合适的概率空间(一般来说就是不同的贴现率),使得某个随机过程(如衍生品价格)是一个鞅,那么定价就容易多了.”这句话貌似在哪里见过，似乎是上林氏哥哥的课上听到的。

不管了，等下学期上到再说

The whole picture of martingale approach to asset pricing

The first aim is to find a self-financing portfolio strategy, i.e. F-previsible process, (φt, ψt) for (St, Bt) which replicates the claim X. We can prove by Ito calculus that the strategy inherently is also self-financing for discounted price process (Zt, 1). The existence of such a strategy is proposed by martingale representation theorem, to implement which we have to make the discounted price process a martingale to begin with. This is where the Cameron-Marton-Giranov theorem comes into play. The theory asserts that there exists a Q measure under which Zt, after transformation, becomes an exponential brownian motion which is a Q-martingale. The drift term γt that transforms the brownian motion component of Zt under P measure to that under Q is (μt-rt)/σt, the market price of risk. According to martingale representation theorem, the expectation of the discounted claim under Q measure can be replicated by a self-financing portfolio strategy. The law of one price makes the expectation the present value of the claim.

哇~~谢谢这么多好心人的解答，虽然我还是没有完全看明白，自己再慢慢着磨啦~~~~~