| Abstract: | Abstract. Using the important case of multi-period investing between a safe asset with a low mean return and an equity basket with a higher total return but a riskier one, this analysis demonstrates that the relevant stochastic programming involves irreducibly recursive variational relations. The "direct" Lagrange-Chow procedure is related to the derivatives of the Bellman "indirect"'algorithms and shown to require essentially the same computations save only for standard integrations or taking of first derivatives. To demonstrate that the comparison is unchanged when a vector of control variables must be optimized in a many-period stochastic scenario, the problem is solved for a rentier to both decide how much to save in each period and how much to put of each period's investment into risky securities. |
