arXiv research

This paper compares ML algorithms for PD prediction, finding XGBoost to be the most effective.

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

As a consequence of the dependence experienced in loan portfolios, the standard binomial test which is based on the assumption of independence does not appear appropriate for validating probabilities of default (PDs). The model underlying the new rules for minimum capital requirements (Basle II) is taken as a point of …

This paper proposes a two-stage scoring approach to help lenders decide their fund allocations in the peer-to-peer (P2P) lending market. The existing scoring approaches focus on only either probability of default (PD) prediction, known as credit scoring, or profitability prediction, known as profit scoring, to identify…

We redefine SICR-events for better loan classification under IFRS 9.

Tutorial on estimating PD using survival analysis under IFRS 9.

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.

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.

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.

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

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.

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

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

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.

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…

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…

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…

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

In this paper we first introduce two new financial products: stock loan and capped stock loan. Then we develop a pure variational inequality method to establish explicitly the values of these stock loans. Finally, we work out ranges of fair values of parameters associated with the loans.

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…

Loan default prediction is one of the most important and critical problems faced by banks and other financial institutions as it has a huge effect on profit. Although many traditional methods exist for mining information about a loan application, most of these methods seem to be under-performing as there have been repo…

Examines how extending home loan durations affects French households financially.

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…

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…

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

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

Two models predict net loan losses using Bayesian and frequentist regression.

Current auto loans converge to super-prime credit despite remaining underwater.

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

We show that there are two homotopy types of PD_3-complexes with fundamental group S_3*_{Z/2Z}S_3, and give explicit constructions for each, which differ only in the attachment of the top cell.

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable…

An integrated and extendable approach for stress-testing loan portfolios

The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincaré duality complexes (PD complexes). The problem is that an arbitrary generalized manifold $X$ is always an ENR space, but it is not necessarily a complex. Moreover, finite PD complexes require the Poincaré dualit…

A stock loan is a loan, secured by a stock, which gives the borrower the right to redeem the stock at any time before or on the loan maturity. The way of dividends distribution has a significant effect on the pricing of the stock loan and the optimal redeeming strategy adopted by the borrower. We present the pricing mo…

In the past few years, there are several researches on Parkinson's disease (PD) recognition using single-photon emission computed tomography (SPECT) images with deep learning (DL) approach. However, the DL model's complexity usually results in difficult model interpretation when used in clinical. Even though there are …

Extends ASRF model for green and brown loans, accounting for systematic and idiosyncratic risks.