Increasing risk: Dynamic mean-preserving spreads

• Published in: Journal of mathematical economics Vol. 86; pp. 69 - 82
• Main Authors: Arcand, Jean-Louis, Hongler, Max-Olivier, Rinaldo, Daniele
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2020; Elsevier Sequoia S.A
• Subjects: Diffusion; Dynamic mean-preserving spreads; Economic analysis; Economic models; Increasing dynamic risk; Integrals; Markov analysis; Markov processes; Noise; Non-Gaussian diffusion; Nonlinear systems; Normal distribution; Probability; Random noise; Stochastic differential equations; Super-diffusive noise source; Transition probabilities; Dynamic mean-preserving spreads; Stochastic differential equations; Super-diffusive noise source; Increasing dynamic risk; Non-Gaussian diffusion
• ISSN: 0304-4068; 1873-1538
• DOI: 10.1016/j.jmateco.2018.11.003

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.