Generalized entropy and model uncertainty

Abstract

I entertain a generalization of the standard Bolzmann-Gibbs-Shannon measure of entropy in multiplier preferences of model uncertainty. Using this measure, I derive a generalized exponential certainty equivalent, which nests the exponential certainty equivalent of the standard Hansen-Sargent model uncertainty formulation and the power certainty equivalent of the popular Epstein-Zin-Weil recursive preferences as special cases. Besides providing a model uncertainty rationale to these risk-sensitive preferences, the generalized exponential equivalent provides additional flexibility in modeling uncertainty through its introduction of pessimism into agents, causing them to overweight events made more likely in the worst case model when forming expectations. In a standard neoclassical growth model, I close the gap to the Hansen-Jagannathan bounds with plausible detection error probabilities using the generalized exponential equivalent and show that Hansen-Sargent and Epstein-Zin-Weil preferences yield comparable market prices of risk for given detection error probabilities.

Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations

“…Some statistical approach based on a Monte‐Carlo or related method 83 combined with an accurate sample path generator 84 will be necessary for approaching this issue. 4.The problem under model ambiguity can be approached from a different mathematical viewpoint, like the generalized entropic penalization approach 85 and nonlinear expectation approach 53 . In the latter case, another zero‐sum game problem can be formulated from a theoretically different viewpoint, especially in problems with several variables 86 .…”