We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities....

Abstract We design a discrete time arbitrage-free model under incomplete information for application to credit risk models in the spirit of Duffie and Lando (2001). We assume a fundamental value process evolving according to a complete market model and a sequence of imperfect signals conveying...

We propose a general treatment of random variables aggregation accounting for the dependence among variables and bounded or unbounded support of their sum. The approach is based on the extension to the concept of convolution to dependent variables, involving copula functions. We show that some...

In this paper, an effectively computable approximation of the price of an American option in a jump-diffusion market model will be shown: results of convergence in Lp and a.s. will be proved.

This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992) [10]. The approach requires the definition of (i) a sequence of distribution functions of the increments of the process, and (ii) a...