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Week 6 Assignment Problem Consider a liquid market with assets B, X, Y where B represents the money market account, that is, B(t) = elo "(s)ds for a short rate r. Assume there exist an equivalent martingale measure Q and Q-Brownian motion W *. (a) Find the Radon-Nikodym derivative dQ do for probability measure Q that makes + a Q-martingale. You need to prove that is indeed a Q-martingale. (b) Assume that dX X = bx (t ) dt + ox(t)dW *(t) dy Y = by(t)dt + or(t)dW *(t) Also assume that there is a Q-Brownian motion WX. Find E such that Y(t) Y(0) &( E . WX ) . X(t) X(0)