FINM345A09Homework5 - FINM345/STAT390 Stochastic Calculus...

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Unformatted text preview: FINM345/STAT390 Stochastic Calculus Hanson Autumn 2009 Lecture 5 Homework (HW5) : Simple and Compound Jump-Diffusions Stochastic Calculus (Due by Lecture 6 in Chalk FINM345 Assignment Submenu) { Note: Dropped the Digital Dropbox } You must show your work, code and/or worksheet for full credit. There are 10 points per question if correct answer and negative points for missing homework sets. 1. Basic Statistics of Linear Simple Jump-Diffusion SDEs with Variable Coefficients: Complete the algebraic IFA exercise for the expectation exercise Theorem 5.1.3, p. L5-p25 (Th. 4.31, p. 119, textbook). Formally prove the following IFA variance theorem using Lemmas 5.1.1 on p. L5- p21 and 5.1.2 on p. L5-p23: Let ( t ), 2 ( t ) and ( t ) j ( t ) for j = 1 : 2 be integrable on [ t , t ]. Then Var[ X ( t )] ifa = x 2 exp 2 Z t t ( ( s ) + ( s ) ( s )) ds exp Z t t ( 2 ( s ) + ( s ) 2 ( s ) ) ds- 1 (1) for the state trajectory X ( t ) given in Eq. (4.37) on p. L4-p50 ((4.78) p. 110) given in Eq....
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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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FINM345A09Homework5 - FINM345/STAT390 Stochastic Calculus...

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