We consider the problem of determining appropriate solvency capital requirements for an insurance company or a financial institution. We demonstrate that the subadditivity condition that is often imposed on solvency capital principles can lead to the undesirable situation where the shortfall...

In this paper we investigate approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S | Lambda ] of S with respect to a conditioning random variable Lambda.The choice for Lambda is...

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...

In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special attention is given to the class of (concave) distortion risk measures. We investigate the relationship...