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

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.