Zheng, Hong HW6

# Zheng, Hong HW6 - CNETzhengh HW6 Zheng Hong November 9,...

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CNETzhengh HW6 Zheng Hong November 9, 2009 Contents 1 Simulate X(t) for the log-normally distributed jump amplitude case 2 2 Ito mean square limit 2 3 Expectation of Mark Deviation Sums 3 4 Variance of X(t) for Linear SDE. 3 1

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1 Simulate X(t) for the log-normally distributed jump amplitude case 0.5 1 1.5 2 r Mark-Jump-Diffusion Simulations t, Time X(t), State 1 X(t), State 5 X(t), State 9 X(t), State 10 XM(t), th. Mean=E[X(t)] XSM(t), Sample Mean Figure 1: log-normally distributed jump amplitude case numean=exp(qparm1+qparm2/2)-1, for = E [ e Q ] - 1 = E [ e σN + μ ] - 1, and N has standard normal distribution. 2 Ito mean square limit R t 0 dW B ( s ) dW S ( s ) ims = lim ms n →∝ Σ n i =0 Δ W B ( t i W S ( t i ) We have known that Cov W B ( t i ) , Δ W S ( t i )] = ρ ( t i t i + O 2 t i ); E [ | Σ n i =0 Δ W B ( t i W S ( t i ) - Σ n i =0 ρ ( t i )Δ( t i ) | ] 6 Σ n i =0 E [ | Δ W B ( t i W S
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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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Zheng, Hong HW6 - CNETzhengh HW6 Zheng Hong November 9,...

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