Distribution and Value of Reserves Using Paid and Incurred Triangles

Many loss reserving models are over-parameterized yet ignore calendar-year (diagonal) effects. Venter [1] illustrates techniques to deal with these problems in a regression environment. Venter [2] explores distributional approaches for the residuals. Gluck [3] shows that systematic effects can increase the reserve runoff ranges by more than would be suggested by models fitted to the triangle data alone. Quarg and Mack [4] show how to get more information into the reserve estimates by jointly using paid and incurred data.

This paper uses the basic idea and data from [4] and the methods of [1] to build simultaneous regression models of the paid and incurred data, including diagonal effects and eliminating non-significant parameters. Then alternative distributions of the residuals are compared in order to find an appropriate residual distribution. To get a runoff distribution, parameter and process uncertainty are simulated from the fitted model. The methods of Gluck [3] are then applied to recognize further effects of systematic risk.

Once the final runoff distribution is available, a possible application is estimating the market value pricing of the reserves. Here this is illustrated using probability transforms, as in Wang [5].

Keywords. Reserving Methods; Reserve Variability; Uncertainty and Ranges, Fair Value, Probability Transforms, Bootstrapping and Resampling Methods, Generalized Linear Modeling.