Question IV: Consider a risky asset X satisfying the following SDE: dX = Xdt + X+dWt....

Transcribed Image Text:

Question IV: Consider a risky asset X satisfying the following SDE: dX = Xdt + X+dWt. The process B = { = ert : t 0} corresponds to the discounting factor. Find the SDE satisfied by the discounted risky asset, Y = X. 3 Hint for Question IV: Sometimes, models include more than one source of uncertainty, e.g., more than one Brownian motion per asset. Also, models could include more than one asset. In these cases, one could use a multidimensional extension of Ito's lemma. dx = K( dt + (*) (*) df(x().. X(m) af k-1 ', t) = axi 1-1 m m i-1 -1 k=1 + ..., X(m), t)dt 182f 2 - (X(1), ..., X (m), t)H(K) H.) dt. Question IV: Consider a risky asset X satisfying the following SDE: dX = Xdt + X+dWt. The process B = { = ert : t 0} corresponds to the discounting factor. Find the SDE satisfied by the discounted risky asset, Y = X. 3 Hint for Question IV: Sometimes, models include more than one source of uncertainty, e.g., more than one Brownian motion per asset. Also, models could include more than one asset. In these cases, one could use a multidimensional extension of Ito's lemma. dx = K( dt + (*) (*) df(x().. X(m) af k-1 ', t) = axi 1-1 m m i-1 -1 k=1 + ..., X(m), t)dt 182f 2 - (X(1), ..., X (m), t)H(K) H.) dt.