In section 13.10.5, we have obtained the explicit solution (13.104)

for the retirement income problem under Gompertz mortality rate from t = 0 until wealth depletion time τ . Show that the solution is consistent with the principle of dynamic optimization; that is, it is also the optimal solution from t = s until wealth depletion time. Hint:

You need to show that the optimal solution on time interval [s , τ] is identical to that given by (13.104) on the same time interval.