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MATH 5050/6815: Homework 5 Due on Tuesday, Apr. 24, beginning of lecture. Problem 1 (1) Compute the quadratic variation of a Poisson(λ) process Nt up to time t. (2) Do problem 9.6 (a), page 230 in you book. You don’t have to solve the differential equation in φ, but 5 points extra credit to whoever does it. Z t Ys d Bs the stochastic integral of Yt Problem 2 Let Y be a simple strategy and Zt = 0 with respect to the Brownian motion. (1) Show that Zt is a martingale with the respect to the Brownian filtration. (2) Show that E(Zt ) = 0. Problem 3 (1) Do Problem 8.5 p.196 in your book. (2) Do Problem 8.6 p.196 in your book. Problem 4 Problem 9.2 , page 229 from your book. 1