Increasing Risk: Dynamic Mean-Preserving Spreads

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 focus on a class of nonlinear scalar diffusion processes, the super-diffusive ballistic process, and prove that it satisfies the integral conditions. We further prove that this class is unique among Brownian bridges. This class of processes 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, workhorse economic models originally based on White Gaussian Noise. A selection of four examples is presented and explicitly solved.

Daniele Rinaldo

Economist, Pianist

My research interests are development and environmental economics. I am currently focusing on the drivers of deforestation in sub-Saharan Africa, on using remote sensing to estimate the economic cost of conflicts, and on natural resource management under regime shifts. Additionally, I work on stochastic processes and probability theory. Also a concert pianist.