General Mean-Field BDSDEs with Stochastic Linear Growth and Discontinuous Generator

In this paper, we consider the general mean-field backward doubly stochastic differential equations (mean-field BDSDEs) whose generator f can be discontinuous in y. We prove the existence theorem of solutions under stochastic linear growth conditions and also obtain the related comparison theorem. N...

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Veröffentlicht in:Mathematics (Basel) 2024-04, Vol.12 (7), p.978
Hauptverfasser: Shi, Yufeng, Wang, Jinghan
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we consider the general mean-field backward doubly stochastic differential equations (mean-field BDSDEs) whose generator f can be discontinuous in y. We prove the existence theorem of solutions under stochastic linear growth conditions and also obtain the related comparison theorem. Naturally, we present those results under the linear growth condition, which is a special case of the stochastic condition. Finally, a financial claim sale problem is discussed, which demonstrates the application of the general mean-field BDSDEs in finance.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12070978