Consider the standard Brownian motion{W(t),t≥0}. Find P(W(1)≥0, W(2)≥0)
Consider the standard Brownian motion{W(t),t≥0}. Find P(W(1)≥0, W(2)≥0)
{ W, : t > 0} be a Brownian motion. Find E(W, (W2t --We), where 0 < t < 1: Let W Select one: t (1 -t) 0
{ W, : t > 0} be a Brownian motion. Find E(W, (W2t --We), where 0
Let W - {Wi,0< t < ) represent a standard Brownian motion Show that the process Z(s)-(zt-W f.0 < t-1) is a standard Brownian motion, where s > 0 is fixed
3. Let W(t be standard Brownian motion and let to > 0. Consider the random variable Min(to) min{W(s) 0 s< to}. Compute the cumulative distribution function of Min(to)
3. Let W(t be standard Brownian motion and let to > 0. Consider the random variable Min(to) min{W(s) 0 s
X(t).12 0 is a standard Brownian motion. Find the distribution of X(t) . 2. Assume that
X(t).12 0 is a standard Brownian motion. Find the distribution of X(t) . 2. Assume that
Consider a market with X W, where W is a Brownian motion process. Define the trading strategy (Vo. ) by vo 1, ,2W Find Gr(p) Select one: WA-T 2WT W2+T
Consider a market with X W, where W is a Brownian motion process. Define the trading strategy (Vo. ) by vo 1, ,2W Find Gr(p) Select one: WA-T 2WT W2+T
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 3+ W3 -3rW, 0 IST. Then p, is equal to Select one: W, W2 3W2-3t - t 3+W
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 3+ W3 -3rW, 0 IST. Then p, is equal to Select one: W, W2 3W2-3t - t 3+W
We consider a Standard Brownian Motion W={Wt,t>=o}, show that
for s<t, Ws|Wt=x the conditional distribution of the process
given a future valueWt=x
We consider a standard Brownian motion W W,t20) Show that for s < t, W /Wt-x the conditional distribution of the process given a future value Wi is given by the following Normal distribution:
8.2. Let W()-X(at)la for a >0. Verify that W(t is also Brownian motion
8.2. Let W()-X(at)la for a >0. Verify that W(t is also Brownian motion
(1) For the standard Brownian motion, (W(t),t2 0], what is the expected first passage time, E(ta), for a > 0, where ta-inf{t : W(t) 2 a]? The following "answers" have been proposed (b) a/2. (c) a (d) 2a (e) None of the above. The correct answer is
8.2. Let W()-X(at)la for a >0. Verify that W(t is also Brownian motion