Robust CARA Optimization

49 Pages Posted: 11 Oct 2021 Last revised: 7 Aug 2023

See all articles by Li Chen

Li Chen

National University of Singapore (NUS)

Melvyn Sim

National University of Singapore (NUS) - NUS Business School

Date Written: October 6, 2021


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 multi-deflected linear decision rules for adaptive optimization models. We also extend the framework to address a multi-period 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 multi-period 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.

Keywords: robust optimization, constant absolute risk aversion, exponential cone programming

JEL Classification: C6, D8

Suggested Citation

Chen, Li and Sim, Melvyn, Robust CARA Optimization (October 6, 2021). Available at SSRN: or

Li Chen (Contact Author)

National University of Singapore (NUS) ( email )

Innovation 4.0, 3 Research Link, Singapore
Singapore, 117602


Melvyn Sim

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592

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