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

Damiano Brigo, Monique Jeanblanc () and Frédéric Vrins
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Monique Jeanblanc: Université d’Evry-Val-d’Essonne

No 2016046, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: Uniformly distributed Stochastic Differential Equation; Conic Martingales; Peacock Process; Uniformly distributed Diffusion; Uniform Martingale Diffusions; Mean Reverting Uniform Diffusion; Mean Reverting Uniform SDE; Maximum Entropy Stochastic Recovery Rates; Maximum Entropy Stochastic Correlation; Uniform SDE Simulation (search for similar items in EconPapers)
Date: 2016-12-09
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions (2020)
Working Paper: SDES with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions (2019)
Working Paper: SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions (2019)
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