A generalized maximin decision model for managing risk and measurable uncertainty

We propose an innovative approach to probabilistic decision making, in which the optimal selection is made both for a decision alternative to manage risk and for a collection of measurable events to simultaneously manage uncertainty as measured by information entropy. The resulting generalized maximin model is a combinatorial optimization problem for maximizing the expected value of a random variable, defined as the minimum return in a given event, over all measurable events in a discrete sample space. The collection of measurable events and applicable probability measure are endogenously determined by a partition of the sample space and optimized for a given index that specifies the number of constituent events. The modeling approach is very general, encompassing as a special case the maximin decision criterion and providing an equivalent solution to the expected value criterion with other cases representing trade-offs between these criteria. A dynamic programming algorithm for solving the non-diversified model in polynomial time is developed. Diversification of the decisions results in a nonlinear integer optimization model that is transformed to an easily solvable mixed-integer linear model. Publicly available data of 79 investments over 10 periods are used to compare the model with mean–variance, conditional value-at-risk, and constrained maximin models.