Bjørn Sundt

Ruin estimates under interest force

Abstract In the present paper we discuss infinite time ruin probabilities in continuous time in a compound Poisson process with a constant premium rate and a constant interest rate. We discuss equations for the ruin probability as well as approximations and upper and lower bounds. Two special cases are treated in more detail: the case with zero initial reserve, and the case with exponential claim sizes.

Further Results on Recursive Evaluation of Compound Distributions

A recent result by Panjer provides a recursive algorithm for the compound distribution of aggregate claims when the counting law belongs to a special recursive family. In the present paper we first give a characterization of this recursive family, then describe some generalizations of Panjers result.

On some Extensions of Panjer's Class of Counting Distributions

In this paper we discuss SOlne properties of counting distributions whose 3 co discrete density {l n},,=0 satisfies a recurslon in the form

ON MULTIVARIATE PANJER RECURSIONS

In the present paper we generalise Panjers (1981) recursion for compound distributions to a multivariate situation where each claim event generates a random vector. We discuss situations within insurance where such models could be applicable, and consider some special cases of the general algorithm. Finally we deduce from the algorithm a multivariate extension of De Prils (1985) recursion for convolutions.

Recursive credibility estimation

Abstract The paper treats models in which credibility estimators may be updated recursively as time passes. It is shown that when updating the credibility estimators, we get their estimation errors updated as a by-product. The models treated include cases with an unknown underlying random parameter that develops over time.

Credibility estimators with geometric weights

Abstract In the present paper we study credibility estimators with geometric weights in the framework of experience rating in motor insurance. We discuss how to find optimal weights. The estimators are compared with the traditional credibility estimators and shown to be more robust against a certain type of violations against the model assumptions. We also discuss advantages and disadvantages relative to ordinary bonus—malus systems.

On bonus systems with credibility scales

Abstract In the present paper we study bonus systems with linear premium scales in a set-up presented in a paper by Borgan, Hoem & Norberg. Some numerical examples are given.

Finite credibility formulae in evolutionary models

Abstract In the present paper we present a recursive procedure for updating of credibility estimators for a class of evolutionary models incorporating the class studied by Kremer (1982). Differing from Kremers procedures the present procedures are based on observations from only a finite past. In the last section the procedure is compared to an approach based on the Kalman filter.

Recursive evaluation of aggregate claims distributions

Abstract In this paper, we give a survey of recursive methods presented in the actuarial literature for exact and approximate evaluation of univariate and multivariate aggregate claims distributions. For the approximations, we present error bounds.

A hierarchical credibility regression model

Abstract The paper develops a hierarchical credibility regression model with random parameters on two levels. The common credibility regression models appear as special cases by assuming one of the parameter levels degenerate. By specializing into another direction we obtain Jewells (1975c) hierarchical model as a special case.