J. Haezendonck

Classical risk theory in an economic environment

Abstract In the present paper the influence of macro-economic factors such as interest and inflation on the classical risk and surplus process is studied.

A martingale approach to premium calculation principles in an arbitrage free market

Abstract An arbitrage free model is used to study martingale equivalent probability distributions on the basic probability space of a compound Poisson process. It is shown how this new approach is related to premium calculation principles.

A new premium calculation principle based on Orlicz norms

Abstract A multiplicative equivalent of the zero utility premium calculation principle is introduced. If the utility function happens to be a normalized Young function the new premium calculation principle is related to Orlicz norms.

Upper bounds on stop-loss premiums in case of known moments up to the fourth order☆

Abstract In actuarial sciences recently a lot of results have been derived for solving the problem sup { E ( X − t ) +: r . υ . X >0,E X ′ = μ , for i = 1, 2, …, k }, x where μ , i = 1 to k as well as t are given. The present contribution solves this problem up to k = 4 analytically.

Numerical best bounds on stop-loss preminus

Abstract The determination of the maximum or minimum of the stop-loss premium E(X − t), (t = retention limit) under various constraints on the distribution of the risk X, leads to linear programs with an infinite number of linear inequality constraints. Retaining a properly chosen increasing finite number of the constraints such a program can be approximated as a sequence of usual finite-dimensional linear programs.

Delay in claim settlement

Abstract In reality there is always a time going by between the moment a claim occurs and the moment of settlement (payment) of that claim. Therefore we introduce the settling delay and the liability process within the framework of an economical environment. We study the main mathematical properties of the liability process. Furthermore we consider some examples.

Premium calculation in insurance

Opening session.- Invited address.- Invited lecture: Some major issues in economics and insurance developments.- Main lectures.- Risk convolution calculations.- Risk sharing, incentives and moral hazard.- State-dependent utility, the demand for insurance and the value of safety.- Separation of risk parameters.- Weighted Markov processes with an application to risk theory.- Practical models in credibility theory, including parameter estimation.- Rate making and the societys sense of fairness.- The impact of reinsurance on the insurers risk.- Chains of reinsurance.- Net stop-loss ordering and related ordering.- Limit theorems for risk processes.- Semi-Markov models in economics and insurance.- Loss distributions: estimation, large sample theory, and applications.- Rating of non proportional reinsurance treaties based on ordered claims.- Resistant line fitting in actuarial science.- Quantitative models of pension costs.- Credibility: estimation of structural parameters.- Short communications.- Population and social security projections for Bangladesh.- Stability of premium principles under maximum entropy perturbations.- Practical rating of variable accident excess-loss premiums.- Motor premium rating.- The mean square error of a randomly discounted sequence of uncertain payments.- Operational time: a short and simple existence proof.- Simulation in actuarial work. Some computational problems.- Bayesian sequential analysis of multivariate point processes.- The actuary in practice.- The influence of reinsurance limits on infinite time ruin probabilities.- Some Berry-Esseen theorems for risk processes.- Some notes on the methods of calculation of life assurance premiums in the United Kingdom.- A stochastic model for investment variables in the United Kingdom.- Inflationary effects on pension plans: wage and benefit patterns.

Ordering of Risks - a Review

In this review we will consider and discuss the most important partial orderings of riks, namely consistent partial ordering and net-stop-loss ordering. More especially we will study the consequencies of ordering of risks for the compound risk: S = X1+X2+···+XN. The impact of orderings of claim size distributions (FX) and claim intensities (FN) on orderings of claim amounts (FS) is examined. The consequencies of these kind of orderings on orderings of risks by means of premium calculation principles is also discussed. In this framework the influence of the dangerousness of distributions on orderings of risks is given. In analogy with the notion of stochastic dominance appearing in the theory of finance, the notion of stop-loss dominance is introduced.

Limit theorems for the present value of the surplus of an insurance portfolio

Abstract It is shown that under general assumptions the present value of the surplus, submitted to macro-economic factors such as interest and inflation, converges to a limit at infinity.

Inversed martingales in risk theory

Abstract The theory of inversed martingales is used in order to prove a generalization of a result of H. Cramer on the probability of non-ruin for a classical surplus process if the initial reserve is positive.