Optimal investment and the ambiguous aggregation of expert opinions
How should a decision-maker assess the potential of an investment when a group of experts provides strongly divergent estimates on its expected payoff? To address this question, we propose and analyze a variant of the well-studied -maxmin model in decision theory. In our framework, and consistent to the paper's empirical focus on R&D investment, experts' subjective probability distributions are allowed to be action-dependent. In addition, the decision maker constrains the sets of priors to be considered in accordance with ethical considerations and/or operational protocols. Using tools from convex and conic optimization, we are able to establish a number of analytical results including a closed-form expression of our model's value function, a thorough investigation of its differentiability properties, and necessary conditions for optimal investment. We apply our framework to original data from a recent expert elicitation survey on solar technology. The analysis suggests that more aggressive investment in solar technology R&D is likely to yield significant dividends even, or rather especially, after taking ambiguity into account. Keywords: expert aggregation; ambiguity; -maxmin; second-order cone programming; renewable energy R&D
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