A stochastic approach for measuring the uncertainty of claims reserves

Abstract

This paper aims to obtain metrics for quantifying the variability of technical provisions for claims by making use of deterministic and stochastic models. In short, everything that the traditional methods do not provide (measures of variability and capital insufficiency) are of fundamental importance for efficient actuarial management. The proposed methodology reveals the probability of insufficiency of the allocated capital to cover the commitments assumed by the insurer. In order to maintain resources to cover the indemnities payable to the insured, insurance companies include technical provisions in their balance sheets. Technical provisions are estimates and are therefore a source of fluctuations in the profit and loss statement of insurers, so understanding and protecting against these adverse variations is fundamental for efficient actuarial management. The stochastic approach enables internal models to be studied for solvency capital, which is a subject that lacks studies in the Brazilian market, and which is determined by a standard model pre-defined by the regulatory body. Stochastic modeling was proposed for Incurred But Not Reported Reserve using bootstrapping and, to validate this approach, the results were compared with the traditional approaches using real Motor Hull and Motor Third Part Liability data from a Brazilian insurance company. There are advantages of adopting stochastic methods instead of deterministic ones to determine technical provisions for claims, since it is possible to empirically estimate the probability distributions. The quantiles of these curves reveal the estimated probability of the real value exceeding a particular level of provisioning in order to extract the probability of capital shortage that the traditional methods do not provide. In addition, the results show that the traditional methods are too conservative, allocating more capital than necessary.