2025/05/23 by Rodosthenous, Neofytos, Zervos, Mihail
#49J10 #49K10 #60G40 #60H30 #93E20 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2505.18394
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running maximum processes. In its original form, the maximality principle identifies an optimal stopping boundary function as the maximal solution to a specific first-order nonlinear ODE that stays strictly below the diagonal in ℝ2. In the context of a suitably tailored optimal stopping problem, we derive a substantial generalisation of the maximality principle: the optimal stopping boundary function is the maximal solution to a specific first-order nonlinear ODE that is associated with a solution to the optimal stopping problem's variational inequality.