Abstract
Given a convex function φ:
R
+ →
R
, the
Csiszár φ-divergence is a function
Iφ:
R
+
n
×
R
+
n
→
R
Iφ (p,q): =
∑
i=1
n
q
i φ
p
i
q
i
I
φ
is a generalized measure of entropy whose distance-like properties make it useful in stochastic optimization and other applications.
We establish relations between
I
φ
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
I
φ
, EU, RCE, and YCE.