Common interest rate models are faced with the problem of volatilities vanishing for spot rates in the vicinity of zero. A possible answer to this difficulty can be given by the introduction of a reflecting boundary at zero, at the same time guaranteeing the spot rate to be non-negative, which...

A subject often recurring in the recent financial and actuarial research, is the investigation of present value functions with stochastic interest rates. Only in the case of uncomplicated payment streams and rather basic interest rate models, an exact analytical result for the distribution...

In financial and actuarial sciences, knowledge about the dependence structure is of a great importance. Unfortunately this kind of information is often scarce. Many research has already been done in this field e.g. through the theory of comonotonicity. It turned out that a comonotonic dependence...

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence. Although our model is developed in a bivariate...

In a paper of 2000, Kaas, Dhaene and Goovaerts investigate the present value of a rather general cash flow. Making use of comonotonic risks, they derive upper and lower bounds for the distribution of the present value. These bounds are very close to the real distribution in case all payments...

The selection of copulas is an important aspect of dependence modeling. In many practical applications, only a limited number of copulas is tested, and the modeling applications usually are restricted to the bivariate case. One explanation is the fact that no graphical copula tool exist which...

In spite of the power of the Black & Scholes option pricing method, there are situations in which the hypothesis of a lognormal model is too restrictive. One possibility to deal with this problem, consists of a weaker hypothesis, fixing only successive moments and eventually the mode of the...

An important part of the current financial and actuarial research deals with the investigation of present value functions in the case of a stochastic interest rate. In the present contribution, it is shown how interest rates can be restricted to meet special types of financial or actuarial...

A key problem in financial and actuarial research, and particularly in the field of risk management, is the choice of models so as to avoid systematic biases in the measurement of risk. An alternative consists of working with incomplete information, by fixing only a number of parameters instead...

In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible,...