Dipartimento di Scienze Statistiche

  Prof. Gian Paolo Clemente Università Cattolica del Sacro Cuore Dipartimento di Discipline Matematiche, Finanza Matematica ed Econometria.   Abstract In non-life insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this seminar, we analyse different stochastic models useful for the evaluation of outstanding claims. As well-known, the literature on claim reserving is very wide. Though limited, we start the analysis by commenting on the research by Thomas Mack, one of the pioneers in this research field. He proposed in (Mack, 1993) a non-parametric way of computing the standard error of the CL method by separating uncertainty on reserve estimation due to the data (Process Error) from uncertainty deriving from the method used to estimate parameters (Estimation Error). Later, in a parametric context, Generalized Linear Models (GLM) have been used to provide both appropriate variability of the reserve estimate and a general inferential set up based on the maximum likelihood approach (see Renshaw and Verrall (1998)). GLM residuals have led the way to a semiparametric bootstrapping procedure. By fitting appropriately incremental payments, this methodology (see England (2002); England and Verrall (1999)) re-samples from the corresponding adjusted Pearson residuals. Practitioners often use a GLM Over-Dispersed Poisson (ODP) model (see England and Verrall (2002)), since this provides estimates close to the standard Chain-Ladder approach used worldwide. In this case, the probability distribution of outstanding claims can be easily derived from the Monte-Carlo procedure. Finally, other deterministic methods, such as Bornhuetter-Ferguson, have been integrated with a stochastic structure aiming at measuring the prediction error of the reserve estimate (Mack, 2008). The aim is to show how these approaches can be useful both in Solvency II framework (see European Commission (2009, 2013, 2015)) and under the new international accounting principles in insurance. Furthermore, since a one-year time horizon for capital requirement evaluation is prescribed by the Solvency II project (European Commission, 2015), we describe how to assess the reserve risk by applying both the market-wide and the undertaking specific approaches provided by the Standard Formula and a partial internal model. On one hand, we will focus on the well-known Merz and Wüthrich formula adopted in the standard formula. On the other hand, we analyse the “re-reserving” method (see Diers (2009) and Ohlsonn and Lauzenings (2008) useful for the application of “one-year” approaches based on the Bootstrap-CL method. To support the description, a case study is developed.     Keywords Claims reserving, capital requirement for reserve risk, one-year view, aggregation and dependence