In this paper we propose a general framework for modeling an insurance liability cash flow in continuous time, by generalizing the reduced-form framework for credit risk and life insurance. In particular, we assume a nontrivial dependence structure between the reference filtration and the insurance internal filtration. We apply these results for pricing and hedging non-life insurance liabilities in hybrid financial and insurance markets, while taking into account the role of inflation under the benchmarked risk-minimization approach. This framework offers at the same time a general and flexible structure, and an explicit and treatable pricing-hedging formula.

One of the most fundamental tasks in non-life insurance, done on regular basis, is risk reserving assessment analysis, which amounts to predict stochastically the overall loss reserves to cover possible claims. The most common reserving methods are based on different parametric approaches using aggregated data structured in the run-off triangles. In this paper, we propose a rather non-parametric approach, which handles the underlying loss development triangles as functional profiles and predicts the claim reserve distribution through permutation bootstrap. Three competitive functional-based reserving techniques, each with slightly different scope, are presented; their theoretical and practical advantages – in particular, effortless implementation, robustness against outliers, and wide-range applicability – are discussed. Theoretical justifications of the methods are derived as well. An evaluation of the empirical performance of the designed methods and a full-scale comparison with standard (parametric) reserving techniques are carried on several hundreds of real run-off triangles against the known real loss outcomes. An important objective of the paper is also to promote the idea of natural usefulness of the functional reserving methods among the reserving practitioners.

We give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

Regression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. This paper is concerned with introducing a general family of mixed Exponential regression models with varying dispersion which can efficiently capture the tail behaviour of losses. Our main achievement is that we present an Expectation-Maximization (EM)-type algorithm which can facilitate maximum likelihood (ML) estimation for our class of mixed Exponential models which allows for regression specifications for both the mean and dispersion parameters. Finally, a real data application based on motor insurance data is given to illustrate the versatility of the proposed EM-type algorithm.

In this paper, we propose a new family of premium calculation principles based on the use of prior information from different sources. Under this framework and based on the use of Ordered Weighted Averaging operators, we provide alternative collective and Bayes premiums and describe some approaches to efficiently compute them. Several examples are detailed to illustrate the performance of the new methods.

In the global insurance market, the number of product-specific policies from different companies has increased significantly, and strong market competition has boosted the demand for a competitive premium. Thus, in the present paper, by considering the competition between each pair of insurers, an N-player game is formulated to investigate the optimal pricing strategy by calculating the Nash equilibrium in an insurance market. Under that framework, each insurer is assumed to maximise its utility of wealth over the unit time interval. With the purpose of solving a game of N-players, the best-response potential game with non-linear aggregation is implemented. The existence of a Nash equilibrium is proved by finding a potential function of all insurers' payoff functions. A 12-player insurance game illustrates the theoretical findings under the framework in which the best-response selection premium strategies always provide the global maximum value of the corresponding payoff function.

Regression techniques are applied to an unbalanced panel data that includes 68 countries observed over a ten-year period, to explore the factors that affect non-life insurance demand across nations. While previous literature has discovered several significant economic, demographic, and institutional variables, little attention has been devoted to cultural dimensions. We find that non-life insurance consumption is adversely impacted in countries where a large fraction of the population has Islamic beliefs. Also highly significant are three of the cultural scores developed by Hofstede in a celebrated study: Power Distance, Individualism, and Uncertainty Avoidance. An important finding is that culture impacts non-life insurance more in affluent countries, with an adjusted R-square coefficient increasing by 11.7%, than in developing countries where the R-square coefficient increase due to cultural impacts is only 1.2%. These results have implications for multinational insurers seeking to enter a new market. Ceteris Paribus, these insurers should target countries, and population segments within these countries, that exhibit low Power Distance, and high Individualism and Uncertainty Avoidance scores.

The International Accounting Standards Board is undertaking a project to develop an Accounting Standard for Insurance. The basis for these proposals is that assets and liabilities should be shown at fair values (market values for quoted instruments). This is an updated version of a paper, prepared by a Working Party established by the General Insurance Research Organisation (GIRO) of the General Insurance Board of the actuarial profession of the United Kingdom, which was first presented to the GIRO Conference in October 2002. This paper summarises and comments upon the principal features of the proposals as they have emerged up to February 2003. The paper considers the implications for general insurance companies of these proposals. In particular, it examines the concept of market value margins, and the practical issues that insurance companies are likely to encounter in implementing them. The emphasis of the paper is on reporting for general insurance business, although many of the principles apply equally to life assurance.