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 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 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...

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...

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...

In most practical cases, it is impossible to find an explicit expression for the distribution function of the present value of a sequence of cash flows that are discounted using a stochastic return process.In this paper, we present an easy computable approximation for this distribution function....

In this paper we present an efficient methodology for approximating the distribution function of the net present value of a series of cash-flows, when the discounting is presented by a stochastic differential equation as in the Vasicek model and in the Ho-Lee model. Upper and lower bounds in...