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In this study, we consider resource allocation problems where the decisions affect multiple beneficiaries and the decision maker aims to ensure that the effect is distributed to the beneficiaries in an equitable manner. We specifically consider stochastic environments where there is u ncertainty in the system and propose a robust programming approach that aims at maximizing system efficiency (measured by the total expected benefit) while guaranteeing an equitable benefit allocation even under the worst scenario. Acknowledging the fact that the robust solution may lead to high efficiency loss and may be over-conservative, we adopt a parametric approach that allows controlling the level of conservatism and present the decision maker alternative solutions that reveal the trade-off between the total expected benefit and the degree of conservatism when incorporating fairness. We obtain tractable formulations, leveraging the results we provide on the properties of highly unfair allocations. We demonstrate the usability of our approach on project selection and shelter allocation applications.