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 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;

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;

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;

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 accurate analytical approximation for the price of a European-style arithmetic Asian option.

For discrete arithmetic Asian options the payoff depends on the price average of the underlying asset. Due to the dependence structure between the prices of the underlying asset, no simple exact pricing formula exists, not even in a Black-Scholes setting. In the recent literature, several approximations and bounds for the price of this type of option are proposed. One of these approximations consists of replacing the distribution of the stochastic price average by an ad hoc distribution (e.g. Lognormal or Inverse Gaussian) with the same first and second moment. In this paper we use a different approach and combine a lower and upper bound into a new analytical approximation. This approximation can be calculated efficiently, turns out to be very accurate and moreover, it has the correct first and second moment. Since the approximation is analytical, we can also calculate the corresponding hedging Greeks and construct a replicating strategy.Options; Dependence; Structure; Prices; Hedging; Strategy;