We present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates. This includes an extension of the Frobenius theorem for Fréchet spaces in particular. This approach puts new light on many of the classical models, such as the Hull-White extended Vasicek and Cox-Ingersoll-Ross short rate models. The notion of a finite dimensional ...

This note contains two main results. (1) (Discrete time) Suppose S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose the initial option prices agree with the Cox–Ross–Rubinstein binomial tree model.) Then S is a geometric simple random walk. (2) (Continuous time) Suppose S = S0eσX−σ 〈X〉/2 is a cont...

The Cox model is now 50 years old. seminal paper of Sir David has had an immeasurable impact on the analysis censored survival data, with applications in many different disciplines. This work also stimulated much additional research diverse areas and led to important theoretical practical advances. These include semiparametric models, nonparametric efficiency, partial likelihood. In addition qu...

In this paper, we present a model in which the default time may coincide with strictly positive probability stopping times reference filtration. One of advantages our construction is that one can choose sequence these times.

As customers are the main asset of any organization, customer churn management is becoming a major task for organizations to retain their valuable customers. In the previous studies, the applicability and efficiency of hierarchical data mining techniques for churn prediction by combining two or more techniques have been proved to provide better performances than many single techniques over a nu...

BACKGROUND Relative survival analysis is a subfield of survival analysis where competing risks data are observed, but the causes of death are unknown. A first step in the analysis of such data is usually the estimation of a net survival curve, possibly followed by regression modelling. Recently, a log-rank type test for comparison of net survival curves has been introduced and the goal of this ...