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问题: 一个硬币, 出现正面的概率为p, 出现反面的概率为 1-p, p !=1/2. 如何制造一个公平的“硬币”。解答: 利用条件概率公式 => P(first coin is head | both coins are different) = p (1-p) / (2p(1-p)) = 1 / 2.同理可知 P(first coin is tail | both coins are different) = p (1-p) / (2p(1-p)) = 1 / 2.所以一个公平的硬币应该是:不停的反转直到连续两次是一正一反,然后看倒数第二次的面向reference: http://s 阅读全文
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Denote g(St ) as the density function of St 看涨欧式期权的价值 C = exp(-r*T) ∫K∞(ST - K)g(ST )dST把上述等式对K求二阶导数, 可得 g(K ) = exp(r*T)∂2C/∂K2 (*)(*)式的一个意义就是butter fly 期权的价值为正 阅读全文
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一些比较重要的定理公式1) If P and Q are equivalent measures, and Xt is an Ft-adapted process then the followingresults hold: EQ (Xt) = EP (Xt dQ/dP)2) Define dQ/dP = exp( - ∫Θdw-1/2∫Θ2du), denote WP is a BM under measure P, then WtQ = WtP +∫0tΘ du is a BM under measure Q 阅读全文
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找到贴吧一个证明 用夹逼定理http://tieba.baidu.com/p/1300488932# 阅读全文