A Generalized Framework for the Stochastic Loss Reserving

The traditional actuarial methods like loss development methods, Bornhuetter-Ferguson method, or Berquist-Sherman method have been served sell as long as point estimates are concerned. Since they are not stochastic approaches, they do not provide confidence intervals which are getting more attention connected to the risk-based capital requirements, explicit discounting the future liabilities, etc. So far, most of the stochastic reserving models which are either in the developing stage or are being used by some companies or organizations, have been explanatory models. The Hoerl curve fitting is their basic formulation. These types of models are fundamentally deficient, because they fit the Hoerl curve to the loss history data. Hoerl curve fitting may be fine, as long as it fits a simple, one dimensional, small series of data to obtain a fitted curve without any statistical implications. If the Hoerl curve fitting method is used with some statistical perspectives in mind, it may produce inconsistent estimates which may not make any sense. In this article, the author suggests a generalized framework which starts by understanding the unique data characteristics of the insurance data. By expanding a Box-Jenkins type time-series model, we developed a generalized framework for modeling a stochastic process on the loss history data. It turned out that some lines are more sensitive to the insurance business cycle than the others. Our contributions will be to provide a generalized framework to derive confidence intervals in which the business cycle was taken into account as well as to provide future estimates for the planning process. This paper is the first step to that direction.