Increasing Risk: Dynamic Mean-Preserving Spreads

2014/12/03 by Arcand, Jean-Louis, Hongler, Max-Olivier, Rinaldo, Daniele
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1412.1384

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.

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