Increasing Risk: Dynamic Mean-Preserving Spreads
  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. 
Jean-Louis Arcand, Max-Olivier Hongler, Daniele Rinaldo
math.PR