In this paper we extend the classical chain-ladder claims reserving method using fuzzy methods. Therefore, we derive new estimators for the claims development factors as well as new predictors for the ultimate claims. The advantage in using fuzzy numbers lies in the fact that the 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 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 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...

These notes are strongly motivated by practitioners who have been seeking for advise in stochastic claims reserving modeling under Solvency 2 and under the Swiss Solvency Test. There have been tremendous developments since the publication of our first book Stochastic Claims Reserving Methods in...

The aim of this contribution is to revisit, clarify and complete the picture of uncertainty estimates in the chain-ladder (CL) claims reserving method. Therefore, we consider the conditional mean square error of prediction (MSEP) of the total prediction uncertainty (using Mack's formula) and the...