arXiv research

The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory p…

A new tree-based estimator, FastPD, efficiently estimates PD functions for machine learning models.

Researchers formalize PD and PFI to relate them to data generating process.

Paper presents a method for estimating long-term PDs with incomplete data.

The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.

The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.

If the probability of default parameters (PDs) fed as input into a credit portfolio model are estimated as through-the-cycle (TTC) PDs stressed market conditions have little impact on the results of the capital calculations conducted with the model. At first glance, this is totally different if the PDs are estimated as…

Paper solves open question about non-positive kernels by decomposing them into PD kernels.

The risk of a credit portfolio depends crucially on correlations between the probability of default (PD) in different economic sectors. Often, PD correlations have to be estimated from relatively short time series of default rates, and the resulting estimation error hinders the detection of a signal. We present statist…

The assessment of Parkinson's disease (PD) poses a significant challenge as it is influenced by various factors which lead to a complex and fluctuating symptom manifestation. Thus, a frequent and objective PD assessment is highly valuable for effective health management of people with Parkinson's disease (PwP). Here, w…

The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution and consider a multi-year case with a …

Tutorial on estimating PD using survival analysis under IFRS 9.

Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not Hilbertian. Indeed, this was recently exemplified in a string of papers which sho…

Develops a PD estimation model using Lévy-driven processes for credit risk.

In banking practice, rating transition matrices have become the standard approach of deriving multi-year probabilities of default (PDs) from one-year PDs, the latter normally being available from Basel ratings. Rating transition matrices have gained in importance with the newly adopted IFRS 9 accounting standard. Here,…

The study examines Cox models for lifetime loan default risk, addressing biased estimates by incorporating recurrent events.

Estimates and quantizes expected persistence diagrams for efficient analysis.

Every $PD_3$-complex bounds a $PD_4$-pair.

PD_3-groups split as HNN extensions, revealing homology class properties.

The study of $PD_3$-pairs extends results for aspherical 3-manifolds.

For credit risk management purposes in general, and for allocation of regulatory capital by banks in particular (Basel II), numerical assessments of the credit-worthiness of borrowers are indispensable. These assessments are expressed in terms of probabilities of default (PD) that should incorporate a certain degree of…

Intuitively, the default risk of a single borrower is higher when her or his assets and debt are denominated in different currencies. Additionally, the default dependence of borrowers with assets and debt in different currencies should be stronger than in the one-currency case. By combining well-known models by Merton …

A possible data source for the estimation of asset correlations is default time series. This study investigates the systematic error that is made if the exposure pool underlying a default time series is assumed to be homogeneous when in reality it is not. We find that the asset correlation will always be underestimated…

Risk management is an important practice in the banking industry. In this paper we develop a new methodology to estimate and predict the probability of default (PD) based on the rating transition matrices, which relates the rating transition matrices to the macroeconomic variables. Our method can overcome the shortcomi…

Study pro-$p$ completions of orientable PD_n groups, proving best results in three cases.

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endo…

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in standard multisymplectic approach to Hamiltonian field the…

The paper classifies PD_4-complexes based on their fundamental group properties.

In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand alone object and discuss its relationship with link diagrams. We give an explicit …

Extends characterization of $PD_3$-pairs with aspherical boundaries to those with spherical boundaries.

We prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always contains a rank 2 free group.

Study extends Elkalla's work on subnormal subgroups to $PD_3$-groups, but $L^2$-Betti numbers need verification.

We define an order relation among oriented $PD_4$-complexes. We show that with respect to this relation, two $PD_4$-complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.

Scaff-PD improves fairness and robustness in federated learning with reduced communication.

PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration approaches and the conditions un…

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the…

New methods estimate point-wise dependency from neural MI models.

We show that the orientable double covering space of an indecomposable non-orientable $PD_3$-complex has torsion free fundamental group.

Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a well-known tool to extract robust topological features, and outputs as \textit{persist…

We show that if $X$ is an indecomposable $PD_3$-complex and $π_1(X) is the fundamental group of a reduced finite graph of finite groups but is not virtually cyclic then$X$is orientable, the underlying graph is a tree, all the edge groups are$Z/2Z$and all but at most one of the vertex groups is dihedral of order$2m…

Unified framework detects changes in complex system models.

Model predicts default risk based on company's financial forecasts and credit conditions.

Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, …

Background: Parkinson's disease (PD) is a prevalent long-term neurodegenerative disease. Though the diagnostic criteria of PD are relatively well defined, the current medical imaging diagnostic procedures are expertise-demanding, and thus call for a higher-integrated AI-based diagnostic algorithm. Methods: In this pape…

Unreduced PDs can perform similarly to reduced PDs in machine learning tasks.

Machine learning classifies Parkinson's Disease stages from walker sensors data.

We study that the $n-$graphs defining by smooth map $f:\Om\subset \ir{n}\to \ir{m}, m\ge 2,$ in $\ir{m+n}$ of the prescribed mean curvature and the Gauss image. We derive the interior curvature estimates $$\sup_{D_R(x)}|B|^2\le\f{C}{R^2}$$ under the dimension limitations and the Gauss image restrictions. If there is no…

Machine learning aids in diagnosing Parkinson's disease with higher accuracy.