Monotone Approximation of Decision Problems

Abstract

Many decision problems exhibit structural properties in the sense that the objective function is a composition of different component functions that can be identified using empirical data. We consider the approximation of such objective functions, subject to general monotonicity constraints on the component functions. Using a constrained B-spline approximation, we provide a data-driven robust optimization method for environments that can be sample-sparse. The method, which simultaneously optimizes and identifies the decision problem, is illustrated for the problem of optimal debt settlement in the credit-card industry.

Keywords: B-Splines, Monotone Approximation, Nonparametric/Semiparametric Methods, Robust Optimization, Sample-Sparse Environments

JEL Classification: C10, C14