Exercise 5 (Each part 2 marks). We showed in class (and in the lecture notes) that the no- arbitrage principle implies the monotonicity principle. Consider the Strong Monotonicity Principle. Let A and B be portfolios and let T > t, where t is the current time. If VA(T) V"(T) with probability one, and VA(T) > VB (T) with positive probability, then VA(t) > VB(). (a) Show that the no-arbitrage principle implies the strong monotonicity principle. (b) Show that the strong monotonicity principle implies the monotonicity principle. (c) Show that the strong monotonicity principle implies the no-arbitrage principle. Hint: If A is an arbitrage portfolio, apply the monotonicity principle to A and an empty portfolio B to deduce a contradiction