Stochastic Re-Reserving in Multi-Year Internal Models -An Approach Based on Simulation

Only high-quality internal models optimally reflecting the risk situation facing the company allow insurers to assess the level of risk capital required. This importantly involves measuring and evaluating reserve risk as a part of insurance risks. In literature there is a wide variety of methods for stochastic reserving such as the Mack method, Bootstrap method, regression approaches, Bayesian methods, etc. All these approaches are based on an ultimo view, so that the uncertainty of full run-off of the liabilities is quantified. In contrast Solvency II requires the quantification of the one-year reserve risk. In addition the investment results, which have to be added to insurance results, are also based on a one-year view, which means that actually many internal models show an ultimo view for insurance results and the one-year view for investment results. So at the moment there is a discussion in academic literature and in insurance practice, how this one-year reserve risk can be quantified. This paper presents the idea of re-reserving which can to be applied in modelling reserve risk and premium risk. Based on this approach we can quantify one-year risk capital and multi-year risk capital. We compare the results of the re-reserving method with the results of the analytic approach recently shown in Merz/Wüthrich (2008).

The second part of this paper deals with the use of multi-year internal models in value and risk-based management. A sample model (based on the re-reserving approach) was applied to test the effectiveness of management strategies on corporate performance indicators such as EVA (economic value added) and RoRAC (return on risk-adjusted capital).

Keywords: Reserve risk, stochastic reserving, re-reserving, Solvency II, internal models, value and risk-based management