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FINM345A09Homework5

# FINM345A09Homework5 - FINM345/STAT390 Stochastic Calculus...

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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 μ ( t ), σ 2 ( t ) and λ ( t ) ν j ( t ) for j = 1 : 2 be integrable on [ t 0 , t ]. Then Var[ X ( t )] ifa = x 2 0 exp 2 t t 0 ( μ ( s ) + λ ( s ) ν ( s )) ds · exp t t 0 ( σ 2 ( s ) + λ ( s ) ν 2 ( s ) ) ds - 1 (1) for the state trajectory X ( t ) given in Eq. (4.37) on p. L4-p50 ((4.78) p. 110 textbook). { Hint: first show partial results by separately showing the the expectation results

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FINM345A09Homework5 - FINM345/STAT390 Stochastic Calculus...

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