We assume that the claims liability process satisfies the distribution-free chain-ladder model assumptions. For claims reserving at time I we predict the total ultimate claim with the information available at time I and, similarly, at time 1 + I we predict the same total ultimate claim with the (updated) information available at time 1 + I . The claims development result at time 1 + I for accounting year ( ] 1 , + I I is then defined to be the difference between these two successive predictions for the total ultimate claim. In [6, 10] we have analyzed this claims development result and we have quantified its prediction uncertainty. Here, we simplify, modify and illustrate the results obtained in [6, 10]. We emphasize that these results have direct consequences for solvency considerations and were (under the new risk-adjusted solvency regulation) already implemented in industry.

/pdf/modelling-the-claims-development-result-for-solvency-4hefrkn5pj.pdf

Modelling The Claims Development Result For Solvency Purposes

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-Wuthrich. The key to these formulas is a recursive representation for the results obtained in Gisler-Wuthrich.

/pdf/recursive-credibility-formula-for-chain-ladder-factors-and-4ls5wv4qab.pdf

Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result

Under new solvency regulations, general insurance companies need to calculate a risk margin to cover possible shortfalls in their liability runoff. A popular approach for the calculation of the risk margin is the so-called cost-of-capital approach. A comprehensive cost-of-capital approach involves the consideration of multiperiod risk measures. Because multiperiod risk measures are rather complex mathematical objects, various proxies are used to estimate this risk margin. Of course, the use of proxies and the study of their quality raises many questions, see IAA position paper [8]. In the present paper we provide a first discourse on multiperiod solvency considerations for a general insurance liability runoff. Within a chain ladder framework, we derive analytic formulas for the risk margin which allow to compare the comprehensive approach to the different proxies used in practice. Moreover, a case study investigates and answers questions raised in [8].

Cost-of-Capital Margin for a General Insurance Liability Runoff

In the work the issue of the pension system sustainability is analyzed in a logical and mathematical framework. A new type of financial management is proposed for Defined Contribution pension scheme (see Angrisani, 2006 and Angrisani, 2008). The novelty is in the introduction of a strucutural funded component in a financial management of PAY-AS-YOU- GO type. The funded component is structurally managed both for the returns on contributions and for the evaluation of the financial sustainability. Therefore it has also the role of reducing the uncovered pension liability at sustainable levels so that the eventual negative demographic effects can be faced. We refer to this type of pension system as Partially Funded Defined Contribution (PFDC) pension system. We show that the two financial management modes, the PAYG part and the funded one, have to interact between them over time so that the sustainability can be ensured. In particular, the intergenerational equity principle will be taken into account. The demographic structure of population underlying the pension system is not represented under specific and fictitious assumptions. Differently from many other works existing in literature, no Steady State hypothesys is used in the proposed model. So taking into account the real demographic dynamics, which can present extremely different patterns over time, the necessity to assure the certainty of pension benefits to the pension system participants is the central key point. This warranty has to be determined by means of specific and fixed rules which principally work on correlation mechanisms between the contribution rate and the demographic and economic dynamics of the pension system. In this framework the proposed model is able to ensure the certainty of the pension system sustainability on the basis of a necessary and sufficient condition. Sustainability indicators of logical-mathematical type are derived from the solution of a differential equation which ensures the no negativity of the pension system assets over time.

Logical indicators for the pension system sustainability

/pdf/study-of-actuarial-characteristics-of-one-year-and-ultimate-1gdeou58.pdf

Study of Actuarial Characteristics of One-Year and Ultimate Reserve Risk Distributions Based on Market Data

Reserve Requirements and Capital Requirements in Non-Life Insurance. An analysis of the Italian MTPL insurance market by stochastic claims reserving models

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Reserve Requirements and Capital Requirements in Non-Life Insurance. An analysis of the Italian MTPL insurance market by stochastic claims reserving models