# On a Class of Optimal Stopping Problems with Applications to Real Option Theory

## TL;DR

This paper develops analytical solutions for a broad class of optimal stopping problems with realistic pay-off functions and negative interest rates, enhancing the modeling of real options and analyzing their sensitivity.

## Contribution

It introduces new analytical solutions for optimal stopping problems with realistic pay-offs and negative interest rates, expanding the applicability in real options theory.

## Key findings

- Analytical solutions for diverse pay-off functions.
- Sensitivity analysis of solutions under various parameters.
- Illustrative economic example highlighting modeling challenges.

## Abstract

We consider an optimal stopping time problem related with many models found in real options problems. The main goal of this work is to bring for the field of real options, different and more realistic pay-off functions, and negative interest rates. Thus, we present analytical solutions for a wide class of pay-off functions, considering quite general assumptions over the model. Also, an extensive and general sensitivity analysis to the solutions, and an economic example which highlight the mathematical difficulties in the standard approaches, are provided.