Solution Algorithms For Dynamic Choquet Expected Utility

Choquet Expected Utility has become increasingly popular as a characterization of uncertainty aversion, choice under probability sub-additivity, and a preference for robustness. In each case, an optimal decision involves the evaluation of the expected utility of an action over a set of probability models that could potentially be relevant, identifying the probability distribution that has the smallest expected utility, then choosing the action that has the largest of these values. In other words, the decision maker maximizes the minimum of possible expected utilities. For quantitative applications of these models, a potentially burdensome intermediate stage of calculations is added to the standard maximization problem. For each candidate for an optimal action, the search over probability models must precede the ranking of the action. For dynamic choice models, this stage of calculation must precede any value-function evaluation.In this paper we develop algorithms for solving discrete-state dynamic programs with Choquet Expected Utility. These algorithms are directly applicable to discrete problems, or can be viewed as approximate solutions to continuous-state problems. Our algorithms rely heavily on the linear-programming approach to nonlinear stochastic dynamic programs developed by Trick and Zin (1992, 1995). We show that given the value-function ordinates, the choice over probability models is the solution to a linear program. For large state spaces these solutions are greatly accelerated through the use of constraint generation algorithms. Further, given the solution of this probability choice, the value-function ordinates that solve Bellman's equations can also be found using linear-programming and constraint generation. We show that this two-step application of dynamic programming is both faster and more accurate than more traditional value-iteration-type algorithms. In addition, we use our algorithms to solve stochastic models of economic growth under Choquet Expected Utility, and contrast the dynamics of these models to traditional von Neumann-Morgenstern Expected Utility models.