Itos Lemma (Multivariate Case) The value (price) of a portfolio of stocks, S(t), follows a geometric Brownian motion process:dS/S =sdt +sdzs while the dividend yield for this portfolio, y(t), follows the process d y = ( S y ) d t + y y 12 d z y where dzs and dzy are standard Brownian motions under P-measure, dzsdzy = dt , and s , s ,, ,andy are positive constants. Solve for the process followed by the portfolios dividends paid per unit time, D(t) = yS.

dS/S = a dt+o,dz while the dividend yield for this portfolio, y(t), follows the process dy = x(yS y)dt+o, ydz, where dz, and dz, are standard Brownian motions under P-measure, dz,dz, = pdt, and Q,, 0,, K, y, and o, are positive constants. Solve for the process followed by the portfolio's dividends paid per unit time, D(t)= yS. dS/S = a dt+o,dz while the dividend yield for this portfolio, y(t), follows the process dy = x(yS y)dt+o, ydz, where dz, and dz, are standard Brownian motions under P-measure, dz,dz, = pdt, and Q,, 0,, K, y, and o, are positive constants. Solve for the process followed by the portfolio's dividends paid per unit time, D(t)= yS