Let W = { Wt : t 0 } be a Brownian motion . Then ,
( Wt ( W2t - Wt2 )) where 0 is
t (t -1 )
So option (1) is correct .
{ 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
You must show your work clearly!!! Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t
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
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
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 the standard Brownian motion{W(t),t≥0}. Find P(W(1)≥0, W(2)≥0)
8.2. Let W()-X(at)la for a >0. Verify that W(t is also Brownian motion
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
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
t2s points). Let B(t) be Brownian motion and let zu) with drift u0. For any B()+ ut be Brownian motion t 0, let T be the first time Z(t) hits a. a) Show that T, is a random time for Z(t) and for B(t). b) Show P(T, 0o)1. c) Use martingale methods to compute E [e-m] for any θ > 0 r> t2s points). Let B(t) be Brownian motion and let zu) with drift u0. For any B()+ ut be...
let {X(t), 1 2 0} denote a Brownian motion 8.1. Let Y(t) = tx(1/t). (a) What is the distribution of Y(t)? (b) Compute Cov(Y(s), Y()) (c) Argue that {Y(t), t 2 0] is also Brownian motion (d) Let Using (c) present an argument that let {X(t), 1 2 0} denote a Brownian motion 8.1. Let Y(t) = tx(1/t). (a) What is the distribution of Y(t)? (b) Compute Cov(Y(s), Y()) (c) Argue that {Y(t), t 2 0] is also Brownian motion...