A generalized maximin decision model for managing risk and measurable uncertainty

Le résumé fourni par la source

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.

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