[Advanced Project] Solve the following lifecycle optimization problem:

Notice that by setting the borrowing rate to be infinite we effectively imposed the no borrowing constraint. We have also removed the mortality-credits term (ξλ_x+t ) from the interest function, because we assume that continuous tontines are not available.

Transcribed Image Text:

max C D e-pu(c+)(px)dt subject to the wealth (budget) constraint F= v(t, F) F + w + b = ct with a given initial Fo > 0 and FD = 0. The wage function is w = wo exp(pt) for t R, while the pension income b, is zero for t R. The valuation rate v = v(t, F) is given by v FO v(t, F) = = , F <0.