# Optimal stopping of one-dimensional diffusions with integral criteria

## TL;DR

This paper characterizes the value function and solutions for an optimal stopping problem involving one-dimensional diffusions with integral criteria, under weak assumptions on the diffusion and integrability conditions.

## Contribution

It provides a comprehensive solution to optimal stopping problems with integral criteria for diffusions under very general conditions.

## Key findings

- Full characterization of the value function
- Solution existence under weak assumptions
- Applicable to a broad class of diffusions

## Abstract

This paper provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion. The results hold under very weak assumptions, namely, the diffusion is assumed to be a weak solution of stochastic differential equation satisfying the Engelbert-Schmidt conditions, while the (stochastic) discount rate and the integrand are required to satisfy only general integrability conditions.