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...

We introduce and discuss a new parametric copula builder which is named the “? construction method”. The methodology is explained and illustrated using 3 types of ? functions. It shows that the ? method has strong visual advantages for recognizing key dependence characteristics and importing...

Consider the problem of computing the optimal lower and upper bound for the expected value E[?(X)], where X is an uncertain random probability variable. This paper studies the case in which the density of X is restricted by multiple shape constraints, each imposed on a different subset of the...

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...

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...

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...