Multi‐year non‐life insurance risk

Abstract

PurposeThe 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/approachThe 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.FindingsThe multi‐year algorithm is applied to the chain ladder reserving model framework of Mack (1993).Practical implicationsThe 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/valueTo 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.