# Tut0 - STAT/ACTSC 446/846 Assignment#1(due 25 January 2008...

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STAT/ACTSC 446/846 Assignment #1 (due 25 January, 2008) Note: When handing in your assignment, please use a cover page showing only your UWID number and sec- tion (lecture) number. Please write your name on the first actual page of your assignment. ACTSC/STAT 846 students: please indicate on the cover page that you are a graduate student by writing “846”. This assignment will be marked over 50 pts. There are 4 bonus marks. But you can’t get more than 50. Problem 1: [2pts] Covariance Let W = { W t ,t 0 } be a standard Brownian motion. Let Z = { Z t ,t 0 } be the Brownian motion with drift μ = 3 and with diffusion coefficient σ = 2 obtained by linear transformation of W . Calculate for t < u the covariance between Z t and W u . Problem 2: [8 pts] Practice of Ito’s Formula Let X t be defined by the SDE (stochastic differential equation): dX t = μdt + σdW t , X 0 = x where W t is a standard Brownian motion. (1) Give an expression of X t (with respect to W t and the parameters). (That amounts to integrate the SDE). Can X t represent the price of a stock?
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