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;

Some results on Denault's capital allocation rule.

Denault (2001) introduces a capital allocation principle where the capital allocated to any risk unit is expressed in terms of the contribution of that risk to the aggregate conditional tail expectation. Panjer (2002) derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman & Valdez (2003) generalize Panjer's result to the class of multivariate elliptical distributions. In this paper we provide an alternative and much simpler proof for the allocation formula in the elliptical case. Further, we show how to derive accurate closed-form approximations for Denault's allocation formula in case of lognormal risks.Capital allocation;

Improved error bounds for approximations to the stop loss transform of compound distributions.

In the present note we deduce a class of bounds for the difference between the stop loss transforms of two compound distributions with the same severity distribution. The class contains bounds of any degree of accuracy in the sense that the bounds can be chosen as close to the exact value as desired; the time required to compute the bounds increases with the accuracy.Distribution;

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;

The safest dependence structure among risks.

In this paper, we investigate the dependence in Frechet spaces containing mutually exclusive risks. It is shown that, under some reasonable assumptions, the safest dependence structure, in the sense of the minimal stop-loss premiums for the aggregate claims involved, is obtained with the Frechet lower bound and precisely corresponds to the mutually exclusive risk of the Frechet space. In that respect, the present paper complements some previous studies by Heilmann (1986), Dhaene & Goovaerts (1996, 1997), Müller (1997) and Taizhong & Zhiqiang (1998). A couple of actuarial applications enhance the interest of the results derived.Dependence; Risk; Structure;

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;