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Probability, Uncertainty and Quantitative Risk
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Article . 2022
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https://dx.doi.org/10.48550/ar...
Article . 2022
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Quadratic mean-field reflected BSDEs

Authors: Hu, Ying; Moreau, Remi; Wang, Falei;

Quadratic mean-field reflected BSDEs

Abstract

<p style='text-indent:20px;'>In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown <inline-formula><tex-math id="M1">\begin{document}$ z $\end{document}</tex-math></inline-formula>. Using a linearization technique and the BMO martingale theory, we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of the <inline-formula><tex-math id="M2">\begin{document}$ \theta $\end{document}</tex-math></inline-formula> -method, we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave (or convex) with respect to the second unknown <inline-formula><tex-math id="M3">\begin{document}$ z $\end{document}</tex-math></inline-formula>.</p>

Country
France
Keywords

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], linearization technique, \(\theta\)-method, 330, mean-field, Probability (math.PR), Applications of stochastic analysis (to PDEs, etc.), reflected BSDEs, 510, Stochastic ordinary differential equations (aspects of stochastic analysis), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], FOS: Mathematics, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Average
Green
gold
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