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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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?
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern