Robust CARA Optimization

We propose robust optimization models and their tractable approximations that cater for ambiguity-averse decision makers whose underlying risk preferences are consistent with constant absolute risk aversion (CARA). Specifically, we focus on maximizing the worst-case expected exponential utility where the underlying uncertainty is generated from a set of stochastically independent factors with ambiguous marginals. To obtain computationally tractable formulations, we propose a hierarchy of approximations, starting from formulating the objective function as tractable concave functions in affinely perturbed cases, developing approximations in concave piecewise affinely perturbed cases, and proposing new multideflected linear decision rules for adaptive optimization models. We also extend the framework to address a multiperiod consumption model. The resultant models would take the form of an exponential conic optimization problem (ECOP), which can be practicably solved using current off-the-shelf solvers. We present numerical examples including project management and multiperiod inventory management with financing to illustrate how our approach can be applied to obtain high-quality solutions that could outperform current stochastic optimization approaches, especially in situations with high risk aversion levels.