Stochastic Loss Reserving in Discrete Time: Individual vs. Aggregate Data Models

Abstract

In this paper, a stochastic individual data model is considered. It accommodates occurrence times, reporting, and settlement delays and severity of every individual claims. This formulation gives rise to a model for the corresponding aggregate data under which classical chain ladder and Bornhuetter–Ferguson algorithms apply. A claims reserving algorithm is developed under this individual data model and comparisons of its performance with chain ladder and Bornhuetter–Ferguson algorithms are made to reveal the effects of using individual data to instead aggregate data. The research findings indicate a remarkable promotion in accuracy of loss reserving, especially when the claims amounts are not too heavy-tailed.

Keywords:

• Aggregate data model
• Bornhuetter–Ferguson algorithm
• Chain ladder algorithm
• Individual data model
• Loss reserving
• Maximum likelihood estimate

Mathematics Subject Classification:

• 62P05