Robust CARA Optimization

Abstract

Decision making under uncertainty involves both ambiguity and risk. In “Robust CARA Optimization,” Chen and Sim have developed innovative optimization models designed for ambiguity-averse decision makers whose risk preference is consistent with constant absolute risk aversion (CARA). The research delves into maximizing the worst-case expected exponential utility amid uncertainties from independent factors with ambiguous marginals. To enhance computational feasibility, the authors developed a series of approximations: starting with tractable concave functions in affinely perturbed cases, advancing to concave piecewise affinely perturbed scenarios, and culminating in novel multi-deflected linear decision rules for adaptive optimization. This comprehensive framework extends to a multi-period consumption model, ultimately forming an exponential conic optimization problem efficiently solvable with existing solvers. Practical applications demonstrated in project and multiperiod inventory management highlight the models’ potential to surpass existing stochastic optimization methods, especially under high risk aversion.