Variable selection plays an important rule in identifying possible factors that could predict the behavior of clients with respect to the bill payments. The Cox model is the standard approach for modeling the time until starting the lack of payments. Parsimony and capacity of predicting are some desirable characteristics of statistical models. This paper aims at proposing a new forward stagewise Lasso (least absolute shrinkage and selection operator) algorithm and applying it for variable selection in the Cox model. The algorithm can be easily extended to run the Adaptive Lasso (ALasso) approach.