SUMMARY Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial...

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

We examine properties of risk measures that can be considered to be in line with some quot;best practicequot; rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk...

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process and a shifted inverse Gaussian process to describe the logarithm of the stock...

In the current contribution, we consider the present value of a series of fixed cash flows under stochastic interest rates. In order to model these interest rates, we don't use the common lognormal model, but stable laws, which better fit in with reality. For this present value, we want to...

A subject often recurring in financial and actuarial papers is the pricing of stocks and securities when the rate of return is stochastic. In most cases, the stocks considered are assumed not to pay out any dividend. In the present contribution we show how it is possible to obtain upper and...

In the recent actuarial literature, several proofs have been given for the fact that if a random vector (X1,X2, . . .,Xn) with given marginals has a comonotonic joint distribution, the sum X1 + X2 + middot; middot; middot; + Xn is the largest possible in convex order. In this note we give a...

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather...

In an insurance context,one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single...

Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we gener alize Yaari's risk measure by relaxing his axioms....