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math.PR2026
A class of Markov processes with resetting and applications to cybersecurity
Giorgia Callegaro, Umut Çetin, Bernardo D'Auria
We introduce a class of piecewise deterministic Markov processes with resetting, motivated by self-exciting models of cyber attacks. Under assumptions reminiscent of ruin theory, w…
math.PR2026
Schrödinger's problem with constraints
Beatrice Acciaio, Umut Çetin
Motivated by the connection between the Kyle equilibrium with static private signal and the Brownian bridge, we study a much broader class of bridges that allow one to consider mor…