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Consider an investor who does not consume or work to earn any labour income. All she does is invest her financial wealth in N +1

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Consider an investor who does not consume or work to earn any labour income. All she does is invest her financial wealth in N +1 assets. The first asset is risk-free with return rudt over the interval [t, t + dt). The remaining N assets are risky and risky asset ne {1,...,N} has return dRnt, where dRn,t = Mn, tdt + on,tdZn,t. Zn is a standard Brownian motion under the physical probability measure P, such that Et[dZi,tdZ;,t] = Pij,tdt for i + j. The investor invests the fraction on,t of her date-t wealth in risky asset n. the return on the investor's portfolio over the interval [t, t+ dt) is given by I NI N dRp,t = (1-> on,t dt+ An,tdRn,t. n = 1 n=1 Hence, show that dRp,t = rdt + (n r1)dt +$.$dZt where Hy = (u1,t, ..., Mn,t)T, 1 = (1, ...,1)T, Et = diag(01,t, ..., 0n,t), pt = (01,t, ..., 0n,t)T, d2+ = (d21,7, ..., dZn,t)T. Consider an investor who does not consume or work to earn any labour income. All she does is invest her financial wealth in N +1 assets. The first asset is risk-free with return rudt over the interval [t, t + dt). The remaining N assets are risky and risky asset ne {1,...,N} has return dRnt, where dRn,t = Mn, tdt + on,tdZn,t. Zn is a standard Brownian motion under the physical probability measure P, such that Et[dZi,tdZ;,t] = Pij,tdt for i + j. The investor invests the fraction on,t of her date-t wealth in risky asset n. the return on the investor's portfolio over the interval [t, t+ dt) is given by I NI N dRp,t = (1-> on,t dt+ An,tdRn,t. n = 1 n=1 Hence, show that dRp,t = rdt + (n r1)dt +$.$dZt where Hy = (u1,t, ..., Mn,t)T, 1 = (1, ...,1)T, Et = diag(01,t, ..., 0n,t), pt = (01,t, ..., 0n,t)T, d2+ = (d21,7, ..., dZn,t)T

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