CERTAINTY EQUIVALENTS AND INFORMATION MEASURES - DUALITY AND EXTREMAL PRINCIPLES

Given a convex function φ: R+ → R, the Csiszár φ-divergence is a function Iφ: R+n × R+n → RIφ (p,q): = ∑ i=1 n qi φ pi qiIφ is a generalized measure of entropy whose distance-like properties make it useful in stochastic optimization and other applications. We establish relations between Iφ and three certainty equivalents, the expected utility (EU), the recourse certainty equivalent (RCE), and Yaari's certainty equivalent (YCE). These relations provide a duality framework for economics of uncertainty and entropy, giving new interpretations and extremal principles for Iφ, EU, RCE, and YCE. © 1970.