A. Guada Azze
We study an Optimal Stopping Problem (OSP) for Gauss–Markov processes conditioned to hit a prescribed terminal distribution. Using a time-space transformation, we show that this OSP is equivalent to that of a Brownian bridge with a random pinning point. This allows us to characterize the optimal stopping time as the first hitting time into the stopping region, and establish continuity of the value function and the free-boundary formulation. We also derive comparison results showing that value functions are ordered by the likelihood-ratio order of terminal densities. When terminal densities are Gaussian or degenerate at a point, the transformed drift simplifies, and optimal stopping boundaries are uniquely characterized by Volterra-type integral equations. Finally, we analyze a two-point terminal distribution, revealing that, despite its apparent simplicity, the stopping region exhibits an unexpectedly complex structure.
Palabras clave: Gauss-Markov bridges, optimal stopping
Programado
Procesos estocásticos
11 de junio de 2025 15:30
Sala VIP Jaume Morera i Galícia