2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64857Various best-choice problems related to the planar homogeneous Poisson process in finite or semi-infinite rectangle are studied. The analysis is largely based on properties of the one-dimensional box-area process associated with the sequence of records. We prove a series of distributional identities involving exponential and uniform random variables, and resolve the Petruccelli-Porosinski-Samuels paradox on coincidence of asymptotic values in certain discrete-time optimal stopping problems.35 pagesProbability60G40, 60G70text