Consider a double-period security market consisting of a bank account with interest rate = 0.2 and one stock. Let the sample space be given by = {1, 2, 3, 4, 5} and let the price of the security be given by

S(0) = 1.8, S(1, 1) = 2.6, S(1, 2) = 2.1, S(1, 3) = 2.1, S(1, 4) = 2.1, S(1, 5) = 2.6, S(2, 1) = 2.7, S(2, 2) = 2.6, S(2, 3) = 1.9, S(2, 4) = 3.1, S(2, 5) = 1.9.

Let

H0(1) = 5, H1(1) = 2, H0(2, 1) = 4.1, H0(2, 2) = 3.6, H0(2, 3) = 3.6, H0(2, 4) = 3.6, H0(2, 5) = 4.1, H1(2, 1) = 2.2, H1(2, 2) = 1.2, H1(2, 3) = 1.2, H1(2, 4) = 1.2,

H1(2, 5) = 2.2.

Show that H = (H0(t), H1(t))t=1,2 is a self-financing trading strategy.