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After decades of experience in developing credit scores, the FICO corporationhas formulated the FICO Credit Scoring Problem as follows: Find the GeneralizedAdditive Model (GAM), with component step functions, that maximizes divergencesubject to the PILE (Palatability, Interpretability, Legal, Explain-ability)constraints. The PILE constraints are also called shape constraints, andsatisfying them is called score engineering. Before 2003, FICO used analgorithm, based on Linear Programing, to approximately solve the FICO CreditScoring Problem. In this paper, I develop an exact solution to the FICO CreditScoring Problem. Finding the exact solution has eluded FICO for years.Divergence is a ratio of quadratic functions of the score weights. I show thatthe max divergence problem can be transformed into a quadratic program. Thequadratic programming formulation allows one to handle the PILE constraintsvery easily. FICO currently uses aspects of this technology to develop thefamous FICO Credit Score.

A Quadratic Programming Solution to the FICO Credit Scoring Problem