5. Consider a two period model with r = 0. For the first period, the stock price is: (S0, S1_): 3 CON 1 At time 1, a dividend Dj is paid and thus S := S- - D1. For the second period, we have S2 := Sf and no dividend is paid, where $ > 0 is a random variable independent of (S1-,D) with EP [] = 1, Varl (E) = 2. We emphasize that we are using P here, not P*. (i) Assume Dj := 8S1- for some constant 8 (0,1). Compute Vo:= sup EP [4D1 + |S212) and find the optimal 8*. 05831 (ii) For general random variable D satisfying 0 > Di 0 is a random variable independent of (S1-,D) with EP [] = 1, Varl (E) = 2. We emphasize that we are using P here, not P*. (i) Assume Dj := 8S1- for some constant 8 (0,1). Compute Vo:= sup EP [4D1 + |S212) and find the optimal 8*. 05831 (ii) For general random variable D satisfying 0 > Di