On Reflection with Two-Sided Jumps

Imane Jarni () and Youssef Ouknine ()
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Imane Jarni: Cadi Ayyad University
Youssef Ouknine: Cadi Ayyad University

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 1811-1830

Abstract: Abstract In the first part of this paper, we pose and solve a new version of Skorokhod problem with jumps, reflected in the half line $$\mathbb {R}^{+}$$ R + and associated to a right limited and left limited function. We show the existence and uniqueness of the solution for this problem. Then, we apply our result to prove existence and uniqueness of solutions of reflected stochastic differential equations driven by optional semimartingales on an unusual probability space.

Keywords: Skorokhod problem; Reflection; Optional semimartingales; Reflecting stochastic differential equations; 60H20; 60G17 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01024-x

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