Description: The estimation of adequate reserves for outstanding claims is one of the main activities of actuaries in property/casualty insurance. The need to estimate future claims has led to the development of many loss reserving techniques. This paper is about the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts. Typically, these negative values will be the result of salvage recoveries, payments from third parties, total or partial cancellation of outstanding claims due to initial overestimation of the loss or to possible favorable jury decision in favor of the insurer, rejection by the insurer, or just plain errors. Some of the traditional methods of claims reserving, such as the chain-ladder technique, may produce estimates of the reserves even when there are negative values. However, many methods can break down in the presence of enough [in number and/or size] negative incremental claims if certain constraints are not met. Historically the chain-ladder method has been used as a gold standard [benchmark], due to its generalized use and ease of application. A method that improves on the gold standard is one that can handle situations where there are many negative incremental claims and/or some of these are large. This paper presents a Bayesian model to consider negative incremental values, based on a three parameter log-normal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. The model applies Markov Chain Monte Carlo [MCMC] using the package WinBUGS.

Description: In this paper the author presents an application of Bayesian forecasting methods to the estimation of reserves for outstanding claims. He assumes that the time number of periods it takes for the claims to be completely paid is fixed and known, that payments are made annually and that the development of partial payments follows a stable pay-off pattern. From Actuarial Research Clearing House, 2003, Vol 1.