Theorem Define X1 via the relationship U' (X1) := IZ U' (*) where I sets X1 as a strategy with an average return of r under B: (35) (36) [1] = x(1+r). Then Xi is the optimal strategy. Discounting is assumed yearly - meaning given r, the present value of 1 dollar in one year is worth 1Hr today. 1. Consider a complete one-period financial model, where maturity equals one year and interest rate equals r = 0.20. At time 1, there are 4 possible outcomes {w1,W2, W3,w4} that in the physical (real) world have been observed to occur with equal probability : An investor has utility function U(X) = (X and optimal terminal capital X1 (wi) = ;2$. Compute the initia, capital of this investor. (50 pts) Answer Theorem Define X1 via the relationship U' (X1) := IZ U' (*) where I sets X1 as a strategy with an average return of r under B: (35) (36) [1] = x(1+r). Then Xi is the optimal strategy. Discounting is assumed yearly - meaning given r, the present value of 1 dollar in one year is worth 1Hr today. 1. Consider a complete one-period financial model, where maturity equals one year and interest rate equals r = 0.20. At time 1, there are 4 possible outcomes {w1,W2, W3,w4} that in the physical (real) world have been observed to occur with equal probability : An investor has utility function U(X) = (X and optimal terminal capital X1 (wi) = ;2$. Compute the initia, capital of this investor. (50 pts)