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Increasing risk: Dynamic mean-preserving spreads

Jean-Louis Arcand (), Max-Olivier Hongler and Daniele Rinaldo

Journal of Mathematical Economics, 2020, vol. 86, issue C, 69-82

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.

Keywords: Increasing dynamic risk; Dynamic mean-preserving spreads; Stochastic differential equations; Non-Gaussian diffusion; Super-diffusive noise source (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.jmateco.2018.11.003

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