The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims developing in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses development factors similar to those of the well-known chain–ladder method. We suggest the Multivariate Skew Normal distribution as a multivariate distribution suitable for modeling these development factors. Empirical analysis using a real portfolio and out-of-sample prediction tests demonstrate the relevance of the model proposed.

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In this paper, the individual claim reserving model proposed by Pigeon et al. (2013) is extended to include paid and incurred data. Analytic expressions are derived for the expected ultimate losses, given observed development patterns. The usefulness of this new model is illustrated using a portfolio of general liability insurance policies. Detailed comparisons with existing approaches reveal that the paid-incurred individual reserving method proposed in this paper performs well and produces more accurate predictions.

The European Commission has introduced new risk management tools in the rural development pillar 2 of the Common Agricultural Policy. One of them consists in providing co-financing support to mutual funds compensating farmers who experience a severe drop in their income. This paper analyses this income stabilisation tool for a region in Belgium by means of a skew normal linear mixed model. Relying on the farm accountancy data network, this analysis focuses on estimating the probability that such a fund would need to intervene and, in that case, the expected amount of each farm income compensation. The predictive distribution of future incomes given past revenues trajectory is derived and used for evaluation purposes. Particular attention is paid to additional requirements that could be imposed to the income stabilisation tool.

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Unearned premium, or more particularly the risk associated to it, has only recently received regulatory attention. Unearned losses occur after the evaluation date for policies written before the evaluation date. Given that an inadequate acquisition pattern of premium and approximate modelling of premium liability can lead to an inaccurate reserve around unearned premium risk, an individual nonhomogeneous loss model including cross-coverage dependence is proposed to provide an alternative method of evaluating this risk. Claim occurrence is analysed in terms of both claim seasonality and multiple coverage frequency. Homogeneous and heterogeneous distributions are fitted to marginals. Copulas are fitted to pairs of coverages using rank-based methods and a tail function. This approach is used on a recent Ontario auto database.

Traditionally, actuaries have used run-off triangles to estimate reserve ("macro" models, on aggregated data). However, it is possible to model payments related to individual claims. If those models provide similar estimations, we investigate uncertainty related to reserves with "macro" and "micro" models. We study theoretical properties of econometric models (Gaussian, Poisson and quasi-Poisson) on individual data, and clustered data. Finally, applications in claims reserving are considered.

In this paper, we propose models for non-life loss reserving combining traditionalapproaches such as Mack’s or generalized linear models and gradient boosting algorithm in anindividual framework. These claim-level models use information about each of the payments madefor each of the claims in the portfolio, as well as characteristics of the insured. We provide an examplebased on a detailed dataset from a property and casualty insurance company. We contrast sometraditional aggregate techniques, at the portfolio-level, with our individual-level approach and wediscuss some points related to practical applications.