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The purpose of this paper is to illustrate the importance of modeling parameter risk in premium risk, especially when data are scarce and a multi-year projection horizon is considered. Internal risk models often integrate both process and parameter risks in modeling reserve risk, whereas parameter risk is typically omitted in premium risk, the modeling of which considers only process risk. We present a variety of methods for modeling parameter risk (asymptotic normality, bootstrap, Bayesian) with different statistical properties. We then integrate these different modeling approaches in an internal risk model and compare our results with those from modeling approaches that measure only process risk in premium risk. We show that parameter risk is substantial, especially when a multi-year projection horizon is considered and when there is only limited historical data available for parameterization (as is often the case in practice). Our results also demonstrate that parameter risk substantially influences risk-based capital and strategic management decisions, such as reinsurance. Our findings emphasize that it is necessary to integrate parameter risk in risk modeling. Our findings are thus not only of interest to academics, but of high relevance to practitioners and regulators working toward appropriate risk modeling in an enterprise risk management and solvency context.

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Purpose -The purpose of this paper is to present a simulation-based approach for modeling multi-year non-life insurance risk in internal risk models. Strategic management in an insurance company requires a multi-year time horizon for economic decision making, for example, in the context of internal risk models. In the literature to date, only the ultimate perspective and, more recently, the one-year perspective (for Solvency II purposes) are considered. Design/methodology/approach -The authors present a way of defining and calculating multi-year claims development results and extend the simulation-based algorithm ("re-reserving") for quantifying one-year non-life insurance risk, presented in Ohlsson and Lauzeningks, to a multi-year perspective. Findings -The multi-year algorithm is applied to the chain ladder reserving model framework of Mack (1993). Practical implications -The usefulness of the new multi-year horizon is illustrated in the context of internal risk models by means of a case study, where the multi-year algorithm is applied to a claims development triangle based on Mack and on England and Verrall. This algorithm has been implemented in an excel tool, which is given as supplemented material. Originality/value -To the best of the authors' knowledge, there are no model approaches or studies on insurance risk for projection periods of not just one, but several, new accident years; this requires a suitable extension of the classical Mack model; however, consideration of multiple years is crucial in the context of enterprise risk management.

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