Speaker: Jasmina Đorđević, University of Niš, Serbia.
Title: Reflected BSDEs with Time-Changed Lévy Noise: Comparing Results under Natural and Enlarged Filtration
Abstract: Stochastic models driven by Lévy noise subject to a random time-change can be applied to phenomena in which the underlying evolution of a system does not unfold in physical time but along a stochastic operational clock — a feature encountered across mathematical finance, turbulence modeling, and biological systems. Reflected backward stochastic differential equations (RBSDEs) provide a natural mathematical framework for such settings, as their solutions can be used to construct dynamic risk measures that respect a prescribed floor, or minimal acceptable level, at every instant, and are further closely connected to problems of stochastic optimal control and optimal stopping. While reflected BSDEs are by now classical tools, the interplay between reflection and time-change — and in particular the role of the filtration carrying information about the clock itself — remains far less understood.
In this talk, we address this gap by studying one-sided reflected BSDEs with a lower barrier driven by time-changed Lévy noise, under the assumption that the time-change is independent of the underlying Lévy process. We establish the existence and uniqueness of solutions under two filtration settings: the natural filtration F generated by the noise, and an enlarged filtration G that carries additional information on the time-change process. A detailed comparison between the two settings is presented, clarifying precisely how the extra information encoded in G shapes the structure and regularity of the solution, with direct implications for the resulting dynamic risk measures. As a further contribution, a comparison principle is established for this class of reflected equations.
Joint work with Prof. Giulia Di Nunno (University of Oslo).
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