We present a novel stochastic model for claims reserving that allows us to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models (Hertig's (1985) model and Gogol's (1993) model ) leading to a log-normal paid-incurred chain (PIC) model....

We present the one-year claims development result (CDR) in the paid-incurred chain (PIC) reserving model. The PIC reserving model presented in Merz and Wüthrich (2010) is a Bayesian stochastic claims reserving model that considers simultaneously claims payments and incurred losses information...

We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium...

It is well known that credibility theory in discrete time is closely related to the discrete technique of Kalman filtering. In this paper we show the close relationship between credibility theory and filter theory in discrete and continuous time as well as between credibility theory in a...

We define a chain ladder model which allows for the study of three different error types: (a) diversifiable process error, (b) non-diversifiable process error, and (c) parameter estimation error. The model is based on the classical stochastic chain ladder model introduced by Mack [Mack, T.,...

The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and...

Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the...

We consider d-dimensional Brownian motion evolving in a scaled Poissonian potential [beta][phi]-2(t)V, where [beta]0 is a constant, [phi] is the scaling function which typically tends to infinity, and V is obtained by translating a fixed non-negative compactly supported shape function to all the...

Tables 2 and 3 in England et al. (2012) raise the conjecture that the claims reserves in the Bayesian over-dispersed Poisson (BODP) model with non-informative gamma priors are equal to the claims reserves in the chain-ladder (CL) model (the small differences in the figures could be explained...