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...

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...

We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of 'constant mix' portfolios.First, we consider the portfolio...

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...

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 analyze and evaluate a standard approach financial institutions use to calculate their so-called total economic capital. If we consider a business that faces a total random loss S over a given one-year horizon then economic capital is traditionally defined as the difference...

We consider a single period portfolio of n dependent credit risks that are subject to default during the period. We show that using stochastic loss given default random variables in conjunction with default correlations can give rise to an inconsistent set of assumptions for estimating the...