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发帖数: 316 | 1 【 以下文字转载自 Quant 讨论区 】
发信人: ccca (cc), 信区: Quant
标 题: 一个百思不得其解 的 Martingale stopping time 问题
发信站: BBS 未名空间站 (Mon Sep 1 11:39:04 2014, 美东)
Problem: B(t) a standard Brownian motion, how is the expecting time it first
hits either -1 or 1.
Solution:
X(t)=exp(B(t)-0.5t) is a martingale. By option sampling theorem, X(t)
stopped at B(t)=-1 or 1 is also a martingale.
Since X(0)=1, we have 0.5*X(1)+0.5*X(-1)=1.
Or exp(1-0.5t)+exp(-1-0.5t)=2,
Or exp(-0.5t)=2/(e+1/e)
Or t = sqrt(-2 ln(2/(e+1/e)).
What is wrong? | Q***5
发帖数: 994 | 2 E(exp^T) not equal exp(E(T)) | a********f
发帖数: 444 | 3 点解要用exponential martingale？
用B_t^2-t不好吗 |
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