The Theory of Split Credibility

This paper tackles the question: why should split credibility be better than credibility without a split? It corrects previous misunderstandings and presents new formulas showing how parameter uncertainty is reduced by use of unsplit credibility and then how it might be further reduced by introduction of a split. It derives the formulas for unsplit and split credibility when losses follow the widely used collective risk model (CRM). It then demonstrates that split credibility can sometimes be ineffective in a CRM context and can sometimes produce negative credibility values or inversions of the primary and excess credibilities. The paper concludes with a call for further research to find a stronger conceptual justification for the split credibility plan used in practice.