Über die Nullstellen homogener Differentialpolynome

In this paper it is discussed for which entire functions g the homogeneous differential polynomial gg-ag² has no zeros. It is shown that g(z)=exp (z+) are the only transcendental entire functions with this property if a1. The case a=1 is indeed exceptional. This result settles a question of Hayman.     

über lokale Maximalbeträge und den Index ganzer Funktionen

Ohne Zusammenfassung     

Über faktorisierbare Lösungen von Riccatischen Differentialgleichungen

Ohne ZusammenfassungHerrn Hans Wittich zum 60. Geburtstag am 4. Mai 1971 gewidmet     

Mixture cure models in credit scoring: If and when borrowers default

Mixture cure models were originally proposed in medical statistics to model long-term survival of cancer patients in terms of two distinct subpopulations - those that are cured of the event of interest and will never relapse, along with those that are uncured and are susceptible to the event. In the present paper, we introduce mixture cure models to the area of credit scoring, where, similarly to the medical setting, a large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. We estimate a mixture cure model predicting (time to) default on a UK personal loan portfolio, and compare its performance to the Cox proportional hazards method and standard logistic regression. Results for credit scoring at an account level and prediction of the number of defaults at a portfolio level are presented; model performance is evaluated through cross validation on discrimination and calibration measures. Discrimination performance for all three approaches was found to be high and competitive. Calibration performance for the survival approaches was found to be superior to logistic regression for intermediate time intervals and useful for fixed 12 month time horizon estimates, reinforcing the flexibility of survival analysis as both a risk ranking tool and for providing robust estimates of probability of default over time. Furthermore, the mixture cure model’s ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower.     

Different growth regimes on prepatterned surfaces: consistent evidence from simulations and experiments

Molecule deposition on a prepatterned substrate is a recently developed technique to generate desired structures of organic molecules on surfaces via self-organization. For the case of prepatterned stripes, the time-resolved process of structure formation is studied via lattice Monte Carlo simulations. By systematic variation of the interaction strength, three distinct growth regimes can be identified: localized growth, bulge formation, and cluster formation. All three growth regimes can be recovered in the experiment when choosing appropriate organic molecules. Some key microscopic observables, reflecting the properties of the structure formation, display a non-monotonous dependence on the interaction strength.     

Modelling LGD for unsecured personal loans: decision tree approach

The New Basel Accord, which was implemented in 2007, has made a significant difference to the use of modelling within financial organisations. In particular it has highlighted the importance of Loss Given Default (LGD) modelling. We propose a decision tree approach to modelling LGD for unsecured consumer loans where the uncertainty in some of the nodes is modelled using a mixture model, where the parameters are obtained using regression. A case study based on default data from the in-house collections department of a UK financial organisation is used to show how such regression can be undertaken.     

Meromorphe Funktionen,die mit ihrer Ableitung Werte teilen

In this paper it is shown that the functions f(z)=e^z are the only nonconstant entire (meromorphic) functions which share two (three) distinct finite values with their derivative.