geometric Brownian motion (7.4.1)
Let S(t) be the geometric Brownian motion (7.4.1) and let Y(t) be the maximum-to-date process (7.4.3). Let T be fixed and let 0 = t0 1 m = T be a partition of [0, T]. Show that as the number of partition points m approaches infinity and the length of the longest subinterval maxj=1 , .. ,m tj – t j-1 approaches zero, the sum
geometric Brownian motion (7.4.1)