Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to derive the distribution of $M_X(t) = \max\limits_{0\leq s\leq t}X(s)$ and $m_X(t) = \min\limits_{0\leq s\leq t}X(s)$, where $dX(t)=\mu X(t) dt+\sigma X(t)dB(t)$ and $B(t)$ is standard Brownian motion. I have seen the derivation of only Brownian motion i.e., $X(t) =\mu dt+\sigma dB(t)$ based on the reflection principle. I am not looking for something rigourous but just reflection principle and change of measure. A diagram will be of much help.

share|improve this question
2  
$\exp$ is monotone and continuous. –  cardinal Jan 13 '12 at 14:03
    
@cardinal, yes how do I proceed –  Vaolter May 18 '12 at 10:12
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.