Mathieu Pigeon

Journal of Statistical Software, 2008

The actuar project is a package of Actuarial Science functions for the R statistical system. The project was launched in 2005 and the package is available on CRAN (Comprehensive R Archive Network) since February 2006. The current version of the package contains functions for use in the fields of risk theory, loss distributions and credibility theory. This paper presents in detail but in non technical terms the most recent version of the package.

2017

Risk theory refers to a body of techniques to model and measure the risk associated with a portfolio of insurance contracts. A first approach consists in modeling the distribution of total claims over a fixed period of time using the classical collective model of risk theory. A second input of interest to the actuary is the evolution of the surplus of the insurance company over many periods of time. In ruin theory, the main quantity of interest is the probability that the surplus becomes negative, in which case technical ruin of the insurance company occurs. The interested reader can read more on these subjects in Klugman et al. (2012); Gerber (1979); Denuit and Charpentier (2004); Kaas et al. (2008), among others. The current version of actuar (Dutang et al., 2008) contains four visible functions related to the above problems: two for the calculation of the aggregate claim amount distribution and two for ruin probability calculations.

Journal of Natural History - J NATUR HIST, 2001

Applied Mathematical Sciences

Recently the classical actuarial risk model for the evaluation of the ruin probability has been generalized to include dependency relations between the claim occurrences times and the claim amounts. For instance it has been incorporated into the stochastic model that the distributions of the times between consecutive claim occurrences times may depend on the last previous claim amount [1] or that claim sizes depend on the past of the point process of instants when claims are presented [2,3]. Results on ruin probabilities and related quantities have been published in several papers under such assumptions. This evolution implies that in a concrete application we have to choose between different versions of the actuarial risk model. This choice should be performed in a reasonable and objective way taking into account our empirical knowledge of the risk process. This leads us naturally to develop statistical tests able to distinguish certain classes of marked point processes. In order to assure the optimal use of the data it seems indicated to look for locally most powerful tests [4] and a clever choice of the period of observation of the risk process greatly facilitates the task and leads to simple procedures which are easy to implement. Keywords: Actuarial risk models, dependencies between claim occurrences times and claim amounts, (locally) most powerful statistical tests, embedded renewal processes, choice of the period of observation of the risk process

This page intentionally left blank Actuarial Mathematics for Life Contingent Risks How can actuaries best equip themselves for the products and risk structures of the future? In this new textbook, three leaders in actuarial science give a modern perspective on life contingencies. The book begins traditionally, covering actuarial models and theory, and emphasizing practical applications using computational techniques. The authors then develop a more contemporary outlook, introducing multiple state models, emerging cash flows and embedded options. Using spreadsheet-style software, the book presents large-scale, realistic examples. Over 150 exercises and solutions teach skills in simulation and projection through computational practice. Balancing rigour with intuition, and emphasizing applications, this textbook is ideal not only for university courses, but also for individuals preparing for professional actuarial examinations and qualified actuaries wishing to renew and update their skills.

Journal of Mathematical Finance, 2016

In this paper, we have used an algorithm to fit the Burr XII distribution to a set of insurance data. As it is well known, the probability of ultimate ruin is obtained as a solution to an integro-differential equation and in case, the claim severity is distributed as Burr XII distribution, this equation has to be solved numerically to obtain an approximation to the probability of ultimate ruin. Two numerical algorithms, namely the stable recursive algorithm and the method of product integration have been used to obtain numerically an approximation to this probability of ultimate ruin. The use of these two numerical algorithms provides a scope for comparing the consistency in values obtained by them. The first two moments of the time to ruin in case of Burr XII distributed claim severity have also been computed using the probability of ultimate ruin obtained through the stable recursive algorithm as an input. All these computations have been done under the assumption of the classical risk model.

Journal of Probability and Statistics, 2010

Understanding actuarial and financial risks poses major challenges. The need for reliable approaches to risk assessment is particularly acute in the present context of highly uncertain financial markets. New regulatory guidelines such as the Basel II Accord for banking and Solvency II for insurance are being implemented in many parts of the world. Regulators in various countries are adopting risk-based approaches to the supervision of financial institutions.

2009

The analyses of insurance risks are an important part of the project of Solvency II preparing of European Commission. The risk theory is the analysis of the stochastic features of non-life insu- rance business. The field of insurance risk theory has grown rapidly. There are now many papers and textbooks, which study the foundations of risk processes along strictly theoretical lines. On the other hand there is a need to develop the theories into forms suitable for practical purposes and to demonstrate their application. Modern computer simulation techniques open up a wide field of practical applications for risk theory concepts, without requiring the restrictive assumptions and sophisticated mathematics, of many traditional aspect of insurance risk theory.. Modelling the size or loss is of crucial importance for an insurer. Particular attention is paid to studying the right tail of the distribution, since it is important to not underestimate the size (and fre- quency) of large losses...

How can actuaries best equip themselves for the products and risk structures of the future? In this new textbook, three leaders in actuarial science give a modern perspective on life contingencies.