Increasing Risk: Dynamic Mean-Preserving Spreads

TL;DR

This paper extends the concept of Mean-Preserving Spreads to a dynamic setting, introducing a unique super-diffusive process that can be used to analyze economic models with more realistic noise structures.

Contribution

It develops a dynamic framework for Mean-Preserving Spreads, characterizes a unique super-diffusive process, and revisits classical economic models with this new approach.

Findings

Identifies a unique super-diffusive process satisfying dynamic mean-preserving conditions.

Provides a simple representation of the process as a superposition of linear Markov processes.

Revisits four economic models using the dynamic mean-preserving spreads framework.

Abstract

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean-Preserving Spreads to a dynamic framework. We adapt the original integral conditions to transition probability densities, and give sufficient conditions for their satisfaction. We then prove that a specific nonlinear scalar diffusion process, super-diffusive ballistic noise, is the unique process that satisfies the integral conditions among a broad class of processes. This process can be generated by a random superposition of linear Markov processes with constant drifts. This exceptionally simple representation enables us to systematically revisit, by means of the properties of Dynamic Mean-Preserving Spreads, four workhorse economic models originally based on White Gaussian Noise.