Decision analysis under ambiguity

• The quantitative implications of modeling of ambiguity attitudes in decision problems is investigated.
• Alternative functionals are nested in decision trees.
• The smooth ambiguity is compared to the minimax and Savage formulations.
• Insights are discussed for analytical and numerical case studies.

In selecting the preferred course of action, decision makers are often uncertain about one or more probabilities of interest. The experimental literature has ascertained that this uncertainty (ambiguity) might affect decision makers’ preferences. Then, the decision maker might wish to incorporate ambiguity aversion in the analysis. We investigate the modeling ambiguity attitudes in the solution of decision analysis problems through functionals well-established in the decision theory literature. We obtain the multiple-event problems for subjective expected utility, smooth ambiguity and maximin decision makers. This allows us to establish the conditions under which these alternative decision makers face equivalent problems. Results for certainty equivalents and risk premia in the presence of both risk and ambiguity aversion are obtained. A recent generalization of the classical Arrow–Pratt quadratic approximation allows us to quantify the portions of a premium due to risk–PLXINSERT-, and to ambiguity-aversion. The numerical implementation of the objective functions is addressed, showing that all functionals can be estimated at no additional burden through Monte Carlo simulation. The well known Carter Racing case study is addressed quantitatively to demonstrate the findings.