*19. Show that \Y(t), t > 0} is a Martingale when Y(t) = cxp{cB(t) - c2t/2]

where c is an arbitrary constant. What is E[Y(t)]l An important property of a Martingale is that if you continually observe the process and then stop at some time Ã, then, subject to some technical conditions (which will hold in the problems to be considered), E[Y(T)] = E[Y(0)]

The time Ô usually depends on the values of the process and is known as a stopping time for the Martingale. This result, that the expected value of the stopped Martingale is equal to its fixed time expectation, is known as the Martingale stopping theorem.