Credit acceptance process strategy case studies - the power of Credit Scoring

The paper is aware of the importance of certain figures that are essential to an understanding of Credit Scoring models in credit acceptance process optimization, namely if the power of discrimination measured by Gini value is increased by 5% then the profit of the process can be increased monthly by about 1 500 kPLN (300 kGBP, 500 kUSD, 350 kEUR). Simple business models of credit loans are also presented: acquisition - installment loan (low price) and cross-sell - cash loans (high price). Scoring models are used to optimize process, to become profitable. Various acceptance strategies with different cutoffs are presented, some are profitable and some are not. Moreover, in a time of prosperity some are preferable whilst the inverse is true during a period of high risk or crisis. To optimize the process four models are employed: three risk models, to predict the probability of default and one typical propensity model to predict the probability of response. It is a simple but very important example of the Customer Lifetime Value (CLTV or CLV) model business, where risk and response models are working together to become a profitable process.Comment: 38 pages, 5 figure

The bicovariant differential calculus on the kappa-Poincare and kappa-Weyl groups

The bicovariant differential calculus on fourdimensional kappa-Poincare group and corresponding Lie-algebra like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional kappa-Weyl group and corresponding Lie-algebra like structure for any matric tensor in the reference frame in which $g_{00}=0$ are considered.Comment: LaTeX, Pages 1

Heat,temperature and relativity

Relativistic thermodynamics as result of some recent computer simulations is derived.Comment: Conference tal

Null K\"ahler structures, Symmetries and Integrability

We review the integrable systems which arise as symmetry reductions of Plebanski's heavenly equations, and their generalisations. We also show that all four-dimensional null Kahler-Einstein (or type N hyper-heavenly) metrics with symmetry can be found from solutions to a variable coefficient generalisation of the dispersionless Kadomtsev-Petviashvili equation.Comment: Text of a talk given at the conference on "Mathematical Physics, General Relativity and Cosmology", held in honour of Professor Jerzy Plebanski. To appear in the Proceeding

Killing Symmetries in H\mathcal{H}-Spaces with Λ\Lambda

All Killing symmetries in complex $\mathcal{H}$-spaces with $\Lambda$ in terms of the Pleba\'nski - Robinson - Finley coordinate system are found. All $\mathcal{H}$-metrics with $\Lambda$ admitting a null Killing vector are explicitly given. It is shown that the problem of non-null Killing vector reduces to looking for solution of the Boyer - Finley - Pleba\'nski (Toda field) equatio

Linear Hilbertian manifold domains

Necessary and sufficient conditions for a dense subspace of a Hilbert space to be a linear Hilbertian manifold domain are given. Some relations between linear Hilbertian manifold domains and domains of self-adjoint operators are found.Comment: 9 pages, Late

On twisting type [N]⊗[N][\textrm{N}] \otimes [\textrm{N}] Ricci flat complex spacetimes with two homothetic symmetries

$\mathcal{HH}$ spaces of type $[\textrm{N}] \otimes [\textrm{N}]$ with twisting congruence of null geodesics defined by the 4-fold undotted and dotted Penrose spinors are investigated. It is assumed that these spaces admit two homothetic symmetries. The general form of the homothetic vector fields are found. New coordinates are introduced which enable us to reduce the $\mathcal{HH}$ system of PDEs to one ODE on one holomorphic function. In a special case this is a second-order ODE and its general solution is explicitly given. In the generic case one gets rather involved fifth-order ODE

Generalized Weyl quantization on the cylinder and quantum phase

Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space $L^2(S^1)$

Consumer finance data generator - a new approach to Credit Scoring technique comparison

This paper aims to present a general idea of method comparison of Credit Scoring techniques. Any scorecard can be made in various methods based on variable transformations in the logistic regression model. To make a comparison and come up with the proof that one technique is better than another is a big challenge due to the limited availability of data. The same conclusion cannot be guaranteed when using other data from another source. The following research challenge can therefore be formulated: how should the comparison be managed in order to get general results that are not biased by particular data? The solution may be in the use of various random data generators. The data generator uses two approaches: transition matrix and scorings. Here are presented both: results of comparison methods and the methodology of these comparison techniques creating. Before building a new model the modeler can undertake a comparison exercise that aims at identifying the best method in the case of the particular data. Here are presented various measures of predictive model like: Gini, Delta Gini, VIF and Max p-value, emphasizing the multi-criteria problem of a "Good model". The idea that is being suggested is of particular use in the model building process where there are defined complex criteria trying to cover the important problems of model stability over a period of time, in order to avoid a crisis. Some arguments for choosing Logit or WOE approach as the best scorecard technique are presented.Comment: 21 pages, 9 figures, 7 table

Notes on thermodynamics in special relativity

Foundations of thermodynamics in special theory of relativity are considered. We argue that from the phenomenological point of view the correct relativistic transformations of heat and absolute temperature are given by the formulae proposed by H. Ott, H. Arzeli\`{e}s and C. M\oller. It is shown that the same transformation rules can be also found from the relativistic Gibbs distribution for ideal gas. This distribution has been recently verified by the computer simulations. Phenomenological and statistical thermometers in relativistic thermodynamics are analysed.Comment: 18 pages. Considerations devoted to accelerated systems exchanging particles have been added. Notation has been improved. References have been added and update