FINM345A09Homework1 - FINM345/STAT390 Stochastic Calculus...

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Unformatted text preview: FINM345/STAT390 Stochastic Calculus Hanson Autumn 2009 Lecture 1 Homework: Stochastic Jump and Diffusion Processes (Due by Lecture 2 in Chalk FINM345 Digital Dropbox) You must show your work, code and/or worksheet for full credit. There are 10 points per question if correct answer. 1. Gaussian Process from Zero Mean Unit Variance Wiener Process: Let { t i : t i +1 = t i + t i ,i = 0 : n,t = 0; t n +1 = T } be a variably spaced partition of the time interval [0 ,T ] with t i > 0. Show the following properties and justify them by giving a reason for every step, such as a property of the process or a property of expectations: (a) Let G ( t ) = t + W ( t ) and G ( t i ) G ( t i + t i )- G ( t i ) with and > constants, then show that E[ G ( t i )] = t i , Var[ G ( t i )] = 2 t i , and Cov[ G ( t i ) , G ( t j )] = 2 t i i,j for i,j = 0 : n , where i,j is the Kronecker delta....
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This note was uploaded on 04/19/2010 for the course FIN 390 taught by Professor Hansen during the Fall '09 term at University of Illinois, Urbana Champaign.

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FINM345A09Homework1 - FINM345/STAT390 Stochastic Calculus...

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