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Correlation uncertainty: a decision-theoretic approach

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  • Gerrit Bauch
  • Lorenz Hartmann

Abstract

We provide a decision-theoretic foundation for uncertainty about the correlation structure on a Cartesian product of probability spaces. Our contribution is two-fold: we first provide a full characterization of the set of possible correlations between subspaces as a convex polytope. Its extreme points are identified as the local maxima of mutual information and as maximally zero probability measures. Second, we derive an axiomatic characterization of preferences narrowing down the set of correlations a decision maker considers, making behavior about correlation testable. Thereby, she may regard collections of subspaces as independent from one another. We illustrate our model and results in simple examples on climate change, insurance and portfolio choice.

Suggested Citation

  • Gerrit Bauch & Lorenz Hartmann, 2025. "Correlation uncertainty: a decision-theoretic approach," Papers 2503.13416, arXiv.org.
    • Handle: RePEc:arx:papers:2503.13416
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    References listed on IDEAS

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