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Increasing risk: Dynamic mean-preserving spreads

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  • Arcand, Jean-Louis
  • Hongler, Max-Olivier
  • Rinaldo, Daniele

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.

Suggested Citation

  • Arcand, Jean-Louis & Hongler, Max-Olivier & Rinaldo, Daniele, 2020. "Increasing risk: Dynamic mean-preserving spreads," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 69-82.
  • Handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:69-82
    DOI: 10.1016/j.jmateco.2018.11.003
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    References listed on IDEAS

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