In the collective risk model, the aggregate claim amount for the portfolio is denoted by S = X1 + X2 + · · · + XN where Xi , i ≥ 1, is the amount of loss resulting from the ith accident and N the total number of accidents incurred by the insurance company during a certain reference period (e.g. one year). Suppose that the amount of a loss is the sum of the claims related to the different covera...

When a given process is seasonal and the seasonal pattern is stable the proportion of events that occur in a given fraction of the total period of the seasonality is constant over time. In this paper we present an application of Bayesian forecasting methods with stable seasonal patterns to insurance claims; specifically to claims incurred but not yet reported, IBNR. We assume that the time it t...

The claims reserves analysis is performed using a Tweedie distribution. Since the aggregate cost per cell of a run-off triangle is generated by a compound distribution, we show that modelling of the variance is important. Dispersion modelling, as well as double GLM theory are not only used to predict the total amount of reserves, but also the mean square error of prediction of the reserves. A n...

In this paper we present an application of Bayesian forecasting methods to outstanding insurance claims. We assume that the time it takes for the claims to be completely paid is fixed and known, that payments are made annually and that the development of partial payments follow a stable pay-off pattern, from one year of origin to another. We present a Bayesian approach to forecasting either the...

An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims on some amount of a scarce resource, but also by some exogenous ex-ante conditions (characteristics), different from claims (e.g., endowments, entitlements, wealth, obligations, assets). Inequalities in the ex-ante conditions induce compensations between agents which influence t...

this paper examines whether combining generalized hyperbolic skew-t distribution, recently introduced in the field of insurance, and extreme value theory (evt) could result in a modeling of loss function that could model central value as well as extreme value in appropriate manner. the data used in this study are the amount of property damage and bodily injury covered under automobile liability...