Claims reserves are held by insurance companies so that they have sufficient funds to pay claims when they are submitted by policyholders. In general insurance, insurance policies usually last for a year; the policyholder pays an upfront premium and then expects any claims to be met - no matter when they are made. The problem for insurers is that there is often a delay before the claims are arrive, and then a further delay before they are paid.

We discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003), whereas Yaari's (1987) dual theory of risk can be viewed as the source of the distortion premium principle (Denneberg (1990), Wang (1996).

External data can often be useful in improving estimation of operational risk loss distributions. This paper develops a systematic approach that incorporates external information into internal loss distribution modelling.

We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models.