Risk theory features of actuar

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. (2008); Gerber (1979); Denuit and Charpentier (2004); Kaas et al. (2001), 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.