Modeling Loss Development with Micro Data

Actuaries have long since recognized the value of survival analysis for calculating case reserves. While there is also a patent connection between setting case reserves and loss development, the tools of survival analysis have been largely ignored in building loss development models. This may be explained in part from history: data storage and computation limitations have traditionally restricted loss development models to aggregated data unsuited to the analysis of individual lives. Until fairly recently, actuarial mathematics has followed an unnecessarily restrictive interpretation of survival analysis. The thesis of this paper is that comparatively recent advances in data processing and in survival analysis theory can be exploited to provide an alternative approach to loss development. Computerized insurance data files now enable automatic production of loss and premium "triangles" directly from individual claim and individual policy rating class exposure data. That suggests building development models directly from micro-data. Moreover, much o f that data is transactional, making it a natural fit to survival analysis models. The idea is to regard paid losses on open claims as "right-censored'" along the lines in which incomplete information is handled in the accelerated failure time models o f bio-statistics and engineering. It is no longer the claimant that represents a "life" but the claim itself with "death" or 'failure" corresponding to claim closure. Also, the paper discusses the use of paid dollars--as well as time--to parameterize the progression from claim emergence to claim closure. The discussion argues that, under this setup, the "expectation of life" plays the role of "case reserve ". The paper considers the application of this case reserve to "develop" paid losses to "ultimate incurred losses ". The main result o f the paper is the proof that this "ultimate loss" model has the correct mean, namely the same mean as the accelerated failure time model, but without the complicating presence of censored observations.