In this paper we present an approach to market based valuation of life insurance policies, in the spirit of the NUMAT proposed by Hans Bühlmann (2002) in an editorial in the ASTIN Bulletin. We have experienced the valuation method for more than one decade, both as a pricing procedure applied to policy portfolios of leading insurance companies, and by including the valuation principles into several actuarial teaching activities.Our interest is mainly focused here on participating policies that in Italy are characterized by contractually binding profit sharing rules. The problem of the fair valuation of the liabilities generated to the insurer by these contracts can be conveniently addressed using the methods of contingent claims pricing. These allow to price correctly the options embedded into the policies and to implement consistent plans of asset-liability management. The approach also provides a market based measurement of the value of business in force for outstanding policy portfolios and consistent assessments of the financial risk based capitals. A NUMAT SYSTEM FROM ITALYIn line with the suggestions expressed by Hans Bühlmann in the proposal of the NUMAT approach (Bühlmann, 2002) and also in the discussion of the article by Aase and Persson (Bühlmann, 2003a), we describe here our experience in applying and teaching the financial approach in valuation of life insurance policies in Italy.Our approach has been focused on two main issues:-providing a mark-to-market (fair) valuation of the outstanding liabilities of an insurance company, jointly with the appropriate measures of sensitivity to financial risk factors, e.g. interest rate risk, that are essential for implementing a consistent plan of asset-liability management; -derive a more reliable measure of the value embedded in business in force (VBIF), including a mark-to-market valuation of the financial options embedded into the policies.It is worth mentioning that when applied to a single policy at the issue date the approach also provides a fair methodology for profit testing. Another

In recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder model studied in Gisler-Wüthrich [9].The key to these formulas is a recursive representation for the results obtained in Gisler-Wüthrich [9]. KEYWORDSClaims reserving, chain ladder method, credibility chain ladder method, claims development result, year end expectation, loss experience prior accident years, liability at maturity, solvency, mean square error of prediction.% % % % % % % % % %

In this paper we present an approach to market based valuation of life insurance policies, in the spirit of the NUMAT proposed by Hans Bühlmann (2002) in an editorial in the ASTIN Bulletin. We have experienced the valuation method for more than one decade, both as a pricing procedure applied to policy portfolios of leading insurance companies, and by including the valuation principles into several actuarial teaching activities.Our interest is mainly focused here on participating policies that in Italy are characterized by contractually binding profit sharing rules. The problem of the fair valuation of the liabilities generated to the insurer by these contracts can be conveniently addressed using the methods of contingent claims pricing. These allow to price correctly the options embedded into the policies and to implement consistent plans of asset-liability management. The approach also provides a market based measurement of the value of business in force for outstanding policy portfolios and consistent assessments of the financial risk based capitals.

We present an approach to individual claims reserving and claim watching in general insurance based on classification and regression trees (CART). We propose a compound model consisting of a frequency section, for the prediction of events concerning reported claims, and a severity section, for the prediction of paid and reserved amounts. The formal structure of the model is based on a set of probabilistic assumptions which allow the provision of sound statistical meaning to the results provided by the CART algorithms. The multiperiod predictions required for claims reserving estimations are obtained by compounding one-period predictions through a simulation procedure. The resulting dynamic model allows the joint modeling of the case reserves, which usually yields useful predictive information. The model also allows predictions under a double-claim regime, i.e., when two different types of compensation can be required by the same claim. Several explicit numerical examples are provided using motor insurance data. For a large claims portfolio we derive an aggregate reserve estimate obtained as the sum of individual reserve estimates and we compare the result with the classical chain-ladder estimate. Backtesting exercises are also proposed concerning event predictions and claim-reserve estimates.

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