Consider a liquid market with assets B, X, Y where B represents the money market account,...

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Consider a liquid market with assets B, X, Y where B represents the money market account, that is, B(t) = el r(s)ds for a short rate r. Assume there exist an equivalent martingale measure Q and Q-Brownian motion W*. dQ (a) Find the Radon-Nikodym derivative for probability measure QX that makes a Q-martingale. You need to prove that is indeed a QX-martingale. (b) Assume that Find such that dX X dY Y = = bx (t)dt + ox (1)dW* (t) = by(t)dt + oy (1)dW* (t) Also assume that there is a QX-Brownian motion W X. Y(t) Y(0) X(t) X(0) = -E₁ (E.Wx). Consider a liquid market with assets B, X, Y where B represents the money market account, that is, B(t) = el r(s)ds for a short rate r. Assume there exist an equivalent martingale measure Q and Q-Brownian motion W*. dQ (a) Find the Radon-Nikodym derivative for probability measure QX that makes a Q-martingale. You need to prove that is indeed a QX-martingale. (b) Assume that Find such that dX X dY Y = = bx (t)dt + ox (1)dW* (t) = by(t)dt + oy (1)dW* (t) Also assume that there is a QX-Brownian motion W X. Y(t) Y(0) X(t) X(0) = -E₁ (E.Wx).

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To find E such that YtXt Y0X0 t E W X we can use the following steps Take the logarithm of both s... View the full answer