On the continuity of optimal stopping surfaces for jump-diffusions

TL;DR

This paper proves the joint continuity of optimal stopping surfaces in two-dimensional jump-diffusion models, under mild assumptions, enhancing understanding of stopping rules in stochastic processes with jumps.

Contribution

It establishes the continuity of optimal stopping surfaces for jump-diffusions, a result previously unknown under mild regularity conditions.

Findings

Optimal stopping surfaces are continuous in time and space.

Continuity holds under mild monotonicity and regularity assumptions.

Results apply to time-inhomogeneous jump-diffusion processes.

Abstract

We show that optimal stopping surfaces $(t,y)\mapsto x_*(t,y)$ arising from time-inhomogeneous optimal stopping problems on two-dimensional jump-diffusions $(X,Y)$ are continuous (jointly in time and space) under mild monotonicity and regularity assumptions of local nature.