Solve the financial planning example with a 72-scenario event tree corresponding to two periods with returns given by  ξ in Table 1 and one period with the original two return realizations given in...

Solve the financial planning example with a 72-scenario event tree corresponding to two periods with returns given by  ξ in Table 1 and one period with the original two return realizations given in Chapter 1. Let the first period solution be x₁
. Solve also for the 72-scenario event tree given by ˜ ξ in Table 2 and let the first period solution be x₁
. To test for their relative performance of these solution, perform a simulation with 1000 runs, where the initial allocations are x₁
and x₁
respectively and the random returns are ξt k for stage t drawn from the underlying lognormal distribution. For each run k = 1,...,1000 , for the second-period allocation, re-solve a two-stage model with input wealth (ξ₁
k )T x₁
and (ξ1 k )T x˜ 1 respectively for the two alternatives and then obtain solutions on the remaining (36-node) sample trees as xk₂
and xk₂
; then, use the second period return ξ₂
k , and repeat for the third and final periods to obtain sample objective values z_k
and z_k
. Compare the distributions of z and  z for these samples by plotting their percentiles. What does this suggest about the use of adjusted samples?