2024/01/23 by Idris Kharroubi, Kharroubi, Idris, Antonio Ocello +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #35J60 #49L20 #49L25 #60G40 #60J80 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2401.12811
openalex publication_date 2024/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using a dynamic programming approach, we characterize the value function for a multiplicative cost, which may depend on the particle's label. We reduce the problem's dimensionality by setting a branching property and defining the problem in a finite-dimensional context. Within this framework, we focus on the value function, establishing uniform continuity and boundedness properties, together with an innovative dynamic programming principle. This outcome leads to an analytical characterization with the help of a nonlinear elliptic PDE. We conclude by showing that the value function serves as the unique viscosity solution for this PDE, generalizing the comparison principle to this setting.