Consider a market with two assets with prices denoted by S1 and S2, which satisfy the stochastic differential equations: dS1(t) = 1S1(t)dt + 1S1(t)d W1(t), dS1(t) = 2S2(t)dt + 2S2(t)d W2(t), where 1,2 are real numbers and 1,2 are positive numbers and W1,W2 are correlated standard Wiener processes with correlation coefficient (1,1), so dW1dW2 = dt. The interest rate is constant, non-negative and denoted by r. Let (S1(T),S2(T)) = max(p1S1(T) + p2S2(T),q1S1(T) + q2S2(T)) denote the pay-off at time T > 0 of a financial derivative, where p1 + p2 = 1,q1 + q2 = 1,p1 > 0,p2 > 0,q1 > 0 and q2 > 0.