tu11 - X t = X exp(0 . 045 t + 0 . 5 B t ) , where X t...

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1. Suppose that X 1 ,X 2 ,... , is a stationary time series with mean μ and ACF ρ ( · ). Show that the best predictor of X n + h of the form aX n + b is obtained by choosing a = ρ ( h ) and b = μ (1 - ρ ( h )). 2. IoA Exam September 2000 Please purchase VeryPDF HTML Converter on http://www.verypdf.com to remove this watermark. Please purchase VeryPDF HTML Converter on http://www.verypdf.com to remove this watermark. 3. Ross: Chapter 10, Q18. Show that { Y ( t ) ,t 0 } is a Martingale when Y ( t ) = B 2 ( t ) - t What is E [ Y ( t )]? Hint: First compute E [ Y ( t ) | B ( u ) , 0 u s ]. 4. A financial analyst models the value of the share index using the model
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Unformatted text preview: X t = X exp(0 . 045 t + 0 . 5 B t ) , where X t denotes the value of the index t years after inception. (a) You are given that X 9 = 8000. Find the probability that X 10 exceeds 10000. 1 (b) What is the variance of the index at time 10 given X 9 = 8000. 5. Ross: Chapter 10, Q19. Show that { Y ( t ) ,t } is a Martingale when Y ( t ) = exp { cB ( t )-c 2 t/ 2 } , where c is an arbitrary constant. What is E [ Y ( t )]? 2...
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tu11 - X t = X exp(0 . 045 t + 0 . 5 B t ) , where X t...

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