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.

(joint work with Manuel Guerra and Carlos Oliveira)