In this paper, we consider the open question on Spearman's rho and Kendall's tau of Nelsen [1991]. Using a technical hypothesis, we can answer in the positive. One question remains open: how can we understand the technical hypothesis? Because this hypothesis is not right in general, we could...

In this paper, we consider the problem of bounds for distribution convolutions and we present some applications to risk management. We show that the upper Frechet bound is not always the more risky dependence structure. It is in contradiction with the belief in finance that maximal risk...

In this paper, we study the approximation procedures introduced by Li, Mikusinski, Sherwood and Taylor [1997]. We show that there exists a bijection between the set of the discretized copulas and the set of the doubly stochastic matrices. For the Bernstein and checkerboard approximations, we...

We consider the problem of modelling the dependence between financial markets. In financial economics, the classical tool is the Pearson (or linear correlation) coefficient to compare the dependence structure. We show that this coefficient does not give a precise information on the dependence...

Copulas are a general tool to construct multivariate distributions and to investigate dependence structure between random variables. However, the concept of copula is not popular in Finance. In this paper, we show that copulas can be extensively used to solve many financial problems

In this paper, we consider non-uniform grids to solve PDE. We derive the theta-scheme algorithm based on finite difference methods and show its consistency. We then apply it to different option pricing problems

In this paper, we consider 2D option pricing. Most of the problems come from the fact that only few closed-form formulas are available. Numerical algorithms are also necessary to compute option prices. This paper examines some topics on this subject

Capital allocation within a bank is getting more important as the regulatory requirements are moving towards economic-based measures of risk. Banks are urged to build sound internal measures of credit and market risks for all their activities. Internal models for credit, market and operational...