Optimal Investment Models with Minimum Consumption Criteria

This paper considers a max-min formulation of multistage optimal investment and consumption problems, with uncertainties in the form of variable productivities of capital and interest rates. The criterion of control performance is minimum consumption over time, weighted by a coefficient which indicates the likelihood of possible disturbance sequences. A dynamic programming method is used. Explicit results for a max-min formulation of the Merton portfolio optimisation problem are obtained. A production-consumption-debt model arising in international finance is also considered