On the characterization of Wang's class of premium principles.

A premium principle is an economic decision rule used by the insurer in order to determine the amount of the net premium for each risk in his portfolio. In this paper we investigate the problem of determining the premium principle to be used. First, we discuss some desirable properties of a premium principle. We prove that the only premium principles that possess these properties belong to a class of premium principles introduced by Wang (1996). Similar results ccan be found in Wang, Young & Panjer (1997)..Principles;

Dependency of risks and stop-loss order.

The correlation order, which is defined as a partial order between bivariate distributions with equal marginals, is shown to be a helpfull tool for deriving results concerning the riskiness of portfolios with pairwise dependencies. Given the distribution functions of the individual risks, it is investigated how changing the dependency assumption influences the stop-loss premiums of such portfolios.Risk; Correlation order; Distribution; Portfolio; Dependency; Functions; Stop-loss premium;

Supermodular ordering and stochastic annuities.

In this paper, we consider several types of stochastic annuities, for which an explicit expression of the distribution function is not available. We will construct a random variable with the same mean and which is larger in stop-loss order, for which the distribution function can be easily obtained.annuities;

On the dependency of risks in the individual life model.

The paper considers several types of dependencies between the different risks of a life insurance portfolio. Each policy is assumed to having a positive face amount (or an amount at risk) during a certain reference period. The amount is due if the policy holder dies during the reference period.First, we will look for the type of dependency between the individuals that gives rise to the riskiest aggregate claims in the sense that it leads to the largest stop-loss premiums. Further, this result is used to derive results for weaker forms of dependency, where the only non-independent risks of the portfolio are the risks of couples (wife and husband).Model; Risk; Dependency; Life insurance; Insurance; Portfolio; Stop-loss premium;

Actuarial applications of financial models.

In the present contribution we indicate the type of situations seen from an insurance point of view, in which financial models serve as a basis for providing solutions to practical problems . In addition, some of the essential differences in the basic assumptions underlying financial models and actuarial applications are given.Actuarial; Applications; Model; Models;

An easy computable upper bound for the price of an arithmetic Asian option.

Using some results from risk theory on stop-loss order and comonotone risks, we show in this paper that the price of an arithmetic Asian option can be bounded from above by the price of a portfolio of European call options.

On the evaluation of 'saving-consumption' plans.

Knowledge of the distribution function of the stochastically compounded value of a series of future (positive and/or negative) payments is needed for solving several problems in an insurance or finance environment, see e.g. Dhaene et al. (2002 a,b). In Kaas et al. (2000), convex lower bound approximations for such a sum have been proposed. In case of changing signs of the payments however, the distribution function or the quantiles of the lower bound are not easy to determine, as the approximation for the random compounded value of the payments will in general not be a comonotonic sum. In this paper, we present a method for determining accurate and easy computable approximations for risk measures of such a sum, in case one first has positive payments (savings), followed by negative ones (consumptions). This particular cashflow pattern is observed in 'saving - consumption' plans. In such a plan, a person saves money on a regular basis for a certain number of years. The amount available at the end of this period is then used to generate a yearly pension for a fixed number of years. Using the results of this paper one can find accurate and easy to compute answers to questions such as: 'What is the minimal required yearly savings effort a during a fixed number of years, such that one will be able to meet, with a probability of at least (1 - e), a given consumption pattern during the withdrawal period ?'Research; Evaluation; Knowledge; Distribution; Value; Problems; Insurance; Approximation; Sign; Quantile; Risk; Risk measure; Consumption; Probability;

Upper and lower bounds for sums of random variables.

In this contribution, the upper bounds for sums of dependent random variables X1 + X2 + … + X n derived by using comonotonicity are sharpened for the case when there exists a random variable Z such that the distribution functions of the Xi, given Z = z, are known. By a similar technique, lower bounds are derived. A numerical application for the case of lognormal random variables is given.Random variable; Variables; Distribution; Functions;