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1answer
63 views

Geometric Brownian motion - Share Prices

The current share price quoted to 30 €. The volatility is 25% per annum. The drift of 5% per annum 1) How is the share price in 6 months probabilistic distributed? 2) The expected value ...
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votes
0answers
37 views

Are my estimates of parameters of geometric brownian motion correct?

I wrote a simulation of a geometric Brownian motion which works like this: $t_i - t_{ i-1 } \sim Exp(\lambda )$ $Z_i \sim N(0,1)$ $Y_i \sim e^{ \sigma \sqrt { t_i - t_{ i-1 } } Z_i +\left( \mu ...
0
votes
1answer
96 views

Strong markov property on max of brownian motion

For $B_t$ Brownian Motion with drift $\mu<0$, I have the max value, $X = \max_{0<t<\infty}B_t$ . I need to prove with the Strong Markov Property that, $P(X>c+d)=P(X>c)P(X>d)$ a. It ...
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2answers
161 views

Max of Brownian motion with drift is finite almost surely

For $B_t$ Brownian Motion with drift $\mu<0$, I need to prove that the max value, $X = \max_{0<t<\infty}B_t$ is finite almost surely, ie $P(X<\infty)=1$. Now, I know that because the mean ...