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.
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