b. Let (, F,F(t), P) be a filtered probability space.

(i) Define what it means for a stochastic process, Mt, to be a martingale on (, F, F(t), P). [3 marks]

(ii) Using the rules of conditional expectation, show that if F(t) is a natural filtration generated by the standard Brownian motion Wt, then,

Mt = e^ Wt ^ 2/ 2 *t is a martingale