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<p>In this paper, we establish the existence and uniqueness of a solution for reflected generalized backward doubly stochastic differential equations with jumps. We consider a generator <i>f</i> satisfying a monotonicity condition and a right-upper-semicontinuous obstacle <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left( \xi _{t}\right) _{0\le t\le T}\)</EquationSource> </InlineEquation>. As an intermediate step, we first prove the existence and uniqueness of a solution under Lipschitz conditions. Our analysis relies on the Mertens decomposition of optional strong supermartingales and the Gal’chouk-Lenglart formula.</p>

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Reflected Generalized BDSDEs with Jumps and a Right-Upper-Semicontinuous Obstacle

  • 期刊论文

  • 发表日期：

    2025年12月20日

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  • Mostapha Abdelouahab Saouli

摘要

In this paper, we establish the existence and uniqueness of a solution for reflected generalized backward doubly stochastic differential equations with jumps. We consider a generator f satisfying a monotonicity condition and a right-upper-semicontinuous obstacle \(\left( \xi _{t}\right) _{0\le t\le T}\) . As an intermediate step, we first prove the existence and uniqueness of a solution under Lipschitz conditions. Our analysis relies on the Mertens decomposition of optional strong supermartingales and the Gal’chouk-Lenglart formula.