Abstract

This work studies the random variable defined by ������:=  ������ ������ ������������'������������������������������, with ������a real matrix of size ������x ������, and ������������is an element of R ������ Gaussian processes. The results show that X is a constant variable when ������������is time-independent. When ������������is an element of R follows a Brownian motion, a closed-form moment generating function (MGF) of X is derived, which does not match the MGFs of known distributions. Finally, a portfolio problem is presented to show how the MGF of X is needed for finding the optimal solution in closed form.