Dynamic Asset Pricing Theory question

carpediem · May 3rd, 2003, 12:23 am

On page 6 of Duffie's book (third edition) has this function: g_theta(\alpha) = U (c + \alpha D^T \theta) Then it passes to : (g_theta(0))' = dU(c)^T * D^T * \theta I do not see where he got the transpose sign on dU(c). Maybe it is very obvious. Can anyone elighten me? Thanks, - Carpe Diem

montecarlo · May 3rd, 2003, 3:29 am

To show that g_theta is maximized at alpha = 0, he took the first order to illustrate the maximum, which is how I imagine dU(c) comes about.

carpediem · May 3rd, 2003, 4:13 pm

Montecarlo, Yes, he took the derivative to find the maximum. However, I do not see why he got dU(c) transposed. Shouldn't it be just dU(c)? Carpe Diem