SDEs with Uniform Distributions : Peacocks, Conic Martingales and Mean Reverting Uniform Diffusions

Brigo, Damiano;Jeanblanc, Monique;Vrins, Frédéric
(2016) , 16 pages

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Authors
  • Brigo, DamianoImperial College London, UK
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  • Jeanblanc, MoniqueUniversité d'Evry-Val-d'Essonne, UMR CNRS 8071
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  • Vrins, Frédéricorcid-logoUCLouvain
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Abstract
We introduce a way to design Stochastic Differential Equations of diffusion type admitting a unique strong solution distributed as a uniform law with general conic time-boundaries. We show that these processes are new diffusion martingales, hence peacocks, and recover two previously known special cases with square-root and linear time-boundaries. We study local time and activity of such processes. We further introduce general mean-reverting diffusion processes having a uniform law at all times evolving between constant boundaries. This may be used to model random probabilities, random recovery rates or random correlations. We verify via an Euler scheme simulation that they have the desired uniform behavior.
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Brigo, D., Jeanblanc, M., & Vrins, F. (2016). SDEs with Uniform Distributions : Peacocks, Conic Martingales and Mean Reverting Uniform Diffusions (CORE Discussion Paper 2016/46). https://hdl.handle.net/2078.5/180055