On the consumption/distribution theorem under the long-run growth criterion subject to a drawdown constraint

Consider any discrete time sequence of investment fortunes Fn which has a finite long-run growth rate when subject to the present value capital drawdown constraint Fne-rn ≥ λ* max0≤k≤nFke-rk, where 0 ≤ λ* < 1, in the presence of a riskless asset affording a return of er dollars per time period per dollar invested. We show that money can be withdrawn for consumption from the invested capital without either reducing the long-run growth rate of such capital or violating the drawdown constraint for our capital sequence, while simultaneously increasing the amount of capital withdrawn for consumption at the identical long-term rate of V(r, λ*). We extend this result to an exponentially increasing number of consumption categories and discuss how additional yearly contributions can temporarily augment the total capital under management. In addition, we assess the short-term practicality of creating such an endowment/consumption/distribution program