Develops EM algorithm for analyzing multi-curve data with switching nonparametric regression models.
problem Analyzing multi-curve data with switching latent state processes.
method Switching nonparametric regression models and an EM algorithm for parameter estimation.
result Frequentist properties of parameter estimates validated through simulation studies and real data application.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
Study multi-curve extension of short rate models with Gaussian factor processes.
problem Derivative pricing in multi-curve financial models.
method Gaussian factor model with short rate and spreads as second order polynomials of Gaussian processes.
result Adjustment factor for pricing linear and optional derivatives in multi-curve setup.
We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship…
Extends multi-curve framework for fully collateralized markets.
problem Lack of a complete multi-currency setup with cross-currency basis.
method Develops a new formulation of currency funding spread and a discretization of the HJM framework.
result Better formulation of currency funding spread for general dependence.
Consistent valuation across different interest rate curves using pricing kernels.
problem Asset pricing with varying discount and cash flow rates.
method Pricing kernel framework linking distinct markets with consistent curve-conversion factors.
result Derivation of an across-curve pricing formula enabling consistent valuation and hedging.
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework w…
Critical graphs of quadratic differentials equidistribute in moduli space.
problem Distribution of critical graphs in moduli space.
method Study of Jenkins-Strebel differentials and their critical graphs.
result Critical graphs equidistribute to the Kontsevich measure.
The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.
problem Dynamics of group actions on SU(2)-representation varieties of surfaces and non-orientable surfaces.
method Description and analysis of group actions generated by Dehn twists on SU(2)-representation varieties.
result Explicit invariant rational functions on SU(2)-representation varieties for specific cases of surfaces and non-orientable surfaces.
The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe the market of interest rate products. On the other hand, using different yield c…
The paper explores using machine learning for yield curve calibration in multiple markets.
problem Calibration challenges in multiple yield curve markets.
method Gaussian process regression and Adam optimizer.
result Good results for single curve markets, but many challenges for multi curve markets.
The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.
problem Characterizing isotopy classes of links in 3-manifolds, especially in contact structures.
method Developed theory of links transverse to a nowhere-zero vector field, constructing examples in both Legendrian and pseudo-Legendrian settings.
result Non-simple isotopy classes of links exist, including Legendrian and pseudo-Legendrian examples.
Counting hyperbolic multi-geodesics with individual component lengths.
problem Counting hyperbolic multi-geodesics with specific component lengths.
method Unified geometric and topological techniques, combining Mirzakhani's results and Margulis's ideas.
result Asymptotic polynomial counts of multi-geodesics in mapping class group orbits, generalizing Wolpert's conjecture.
We show that any grafting ray in Teichmüller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichmüller geodesic ray. As a consequence the projection of a generic grafting ray to moduli space is dense. We also show that the set of points in Teichmüller space obtained by integ…
Formula connects linking number to spectral theory on 3-torus.
problem Computing linking number of multi-geodesics on 3-torus.
method Spectral theory of Laplace operator on differential forms.
result Formula for linking number of multi-geodesics on 3-torus.
For a long time interest-rate models were built on a single yield curve used both for discounting and forwarding. However, the crisis that has affected financial markets in the last years led market players to revise this assumption and accommodate basis-swap spreads, whose remarkable widening can no longer be neglecte…
Develops a new model for multiple yield curves using branching processes.
problem Reproduce empirical features of spreads between interbank rates.
method Continuous-state branching processes with immigration (CBI processes).
result Models can generate contagion effects among different spreads.
Unified framework for multiple yield curve models using affine processes.
problem Consolidation of various multiple yield curve modeling approaches.
method Modeling Libor rates and OIS rates as functions of an underlying affine process.
result Tractable valuation formulas and new model developments.
Study minima of geodesic lengths for specific curves on surfaces.
problem Finding the shortest geodesic paths on surfaces.
method Using curves related to dessins d'enfants and Grothendieck-Belyi surfaces.
result Minima of geodesic lengths are achieved on Riemann surfaces defined over number fields.
Geometric interpretation of 3-manifold invariants using immersed curves.
problem Obstructing smooth equivalences between 4-manifolds and surfaces with boundary.
method Relating morphisms between bordered Floer invariants to cobordism maps via immersed curves in the punctured torus.
result Morphisms between immersed curve invariants compute certain cobordism maps.
In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one…
Extends classification of invariant measures on geodesic currents.
problem Classifying invariant measures on geodesic currents.
method Decomposition of currents into measured laminations, multi-curves, and bound currents.
result Extension of classification to geodesic currents.
Constructs rational models for pricing and managing inflation-linked derivatives.
problem Pricing and risk management of inflation-linked derivatives.
method Rational models constructed in a multiplicative manner, isolating inflation convexity-adjustment.
result Closed-form pricing of various inflation products and exotic swaps.
Paper studies metric ribbon graphs and provides a recursion for their volumes.
problem Calculating volumes of combinatorial moduli spaces of directed metric ribbon graphs.
method Decomposes directed ribbon graphs into simpler graphs with one vertex, proving a canonical recursion scheme for volumes.
result Explicit recursion for volumes of four-valent metric ribbon graphs provided.
The study bounds distances in simplicial complexes and defines new invariants for 3-manifolds and handlebody-knots.
problem Estimating distances in simplicial complexes associated with low-dimensional manifolds.
method Obtained bounds on distances in simplicial complexes using topological conditions on vertices and curve complexes. Defined new invariants for 3-manifolds and handlebody-knots using splitting distances.
result Splitting distances in simplicial complexes are bounded from below under stabilizations, leading to converging invariants.
Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous, they depend on input distributions that are data-cleaning- and Data-Model-depende…
This paper studies a subgroup of the Goeritz group related to Heegaard splittings induced by openbook decompositions.
problem Understanding the subgroup of the Goeritz group associated with Heegaard splittings from openbook decompositions.
method Analyzes the mapping class group of a 3-manifold, focusing on elements that preserve the binding and commute with the monodromy.
result Characterizes the Goeritz group subgroup as a quotient of specific mapping class groups and provides a criterion for certain elements.
Paper examines pricing and hedging for cross-currency swaps referencing backward-looking rates.
problem Pricing and hedging cross-currency swaps with backward-looking rates.
method Uses interest rate and currency futures for hedging, analyzes arbitrage-free multi-curve setting.
result Explicit pricing and hedging results for CCBS with backward-looking rates.
This study tackles XVA model risk and computational effort in derivatives pricing.
problem XVA model risk and computational effort in derivatives pricing, especially for counterparty and funding risk.
method Realistic and complete XVA modelling framework based on multi-curve time-dependent volatility G2++ stochastic dynamics, calibrated on real market data, and multi-step Monte Carlo simulation.
result Identification and quantification of model risk sources and computational effort in XVA figures.
New combinatorial structures for Teichmüller spaces with Thurston's metric are explored.
problem Understanding the combinatorial structures of Teichmüller spaces with Thurston's metric.
method Analyzing the unit tangent and cotangent spheres of Teichmüller space, proving formulas for dimensions and codimensions of faces.
result The combinatorial structure of unit spheres in Teichmüller spaces is independent of the underlying point and is isomorphic to the extended mapping class group.
Proposes RSP model for efficient big data analysis.
problem Efficiently partitioning big data sets for analysis.
method Random sample partition (RSP) data model and block-level sampling.
result RSP data blocks can estimate statistics and build models equivalent to whole data set.
Data preprocessing improves data quality for robust data mining.
problem Noisy and incomplete data hinders data mining models.
method Overview of data cleaning, transformation, and preprocessing methods.
result Preprocessing significantly affects data mining model performance.
A new method for handling imbalanced big data using ensembles and smart data.
problem Imbalanced data distribution in big data scenarios.
method Smart Data driven Decision Trees Ensemble (SD_DeTE) methodology.
result SD_DeTE outperforms Random Forest in handling imbalanced binary classification problems in big data.
Prevents sensitive data generation in diffusion models using labeled and unlabeled data.
problem Generating sensitive data in diffusion models using unlabeled data.
method Positive-Unlabeled Diffusion Models, approximating ELBO with labeled and unlabeled data.
result Prevents the generation of sensitive data without compromising image quality.
Study reveals Data Shapley's inconsistent performance in data selection tasks.
problem Inconsistency of Data Shapley's performance in data selection across different settings.
method Hypothesis testing framework and identification of utility functions.
result Data Shapley's performance is no better than random selection without specific constraints.
Survey on data collection challenges in machine learning.
problem Data scarcity and need for labeled data in machine learning.
method Comprehensive study of data acquisition, labeling, and improvement techniques.
result Identification of research challenges in data collection.
PRRO generates synthetic tabular data that improves SL performance and class distribution.
problem Low SL utility of synthetic data due to class imbalance and overlooked data relationships.
method Data pruning and column reordering to optimize SL utility.
result Synthetic data generated with PRRO enhances predictive performance and class distribution.
Defines data science as a natural ecosystem with challenges and missions.
problem Challenges and missions in data science due to 5D complexities and data life cycle phases.
method Systemic and data-centric view of data science as a fusion of data universe and its challenges, formalizing a general-purpose architecture.
result Essential data science as a natural ecosystem integrating specific disciplines and high-impact applications.
Synthetic data enhances analytics but requires careful volume management.
problem Accuracy of statistical methods on synthetic data vs. raw data.
method Synthetic Data Generation for Analytics framework using tabular diffusion models.
result Error rate decreases with more synthetic data but may stabilize or increase.
Data science redefines causal inference from observational data, classifying tasks into description, prediction, and counterfactual prediction.
problem Widespread misunderstandings about data science's role in causal inference from observational data.
method Organizing data science tasks into three classes: Description, prediction, and counterfactual prediction (including causal inference).
result The necessity of subject-matter expert knowledge for causal analyses in data science.
This paper evaluates how dirty data affects data mining and machine learning results.
problem Negative impacts of dirty data on data mining and machine learning results.
method Experimental comparison of missing, inconsistent, and conflicting data on classification and clustering algorithms.
result Guidelines for algorithm selection and data cleaning based on experimental findings.
DPASF stream preprocesses Big Data streams efficiently.
problem Efficient preprocessing of streaming Big Data.
method Implemented six preprocessing algorithms in Apache Flink.
result Preprocessing improves data accuracy in streaming Big Data.
This paper introduces C-DSL to improve data mining outcomes by considering context.
problem Data collection ambiguities, data imbalance, hidden biases, lack of domain info, and data incompleteness.
method Developed Context-Driven Data Science Lifecycle (C-DSL) to address data quality issues.
result Tangible improvements to data mining outcomes were achieved through C-DSL.
Proposes using probabilistic models for privacy-preserving synthetic data.
problem Designing high-quality synthetic data for privacy preservation.
method Formulate the problem through probabilistic modelling, choosing a model for the data.
result Statistical discoveries can be reliably reproduced from synthetic data.
Unlabeled data helps stop active learning better than labeled data.
problem Reducing the need for manual annotation in text classification.
method Compared stopping methods based on labeled, unlabeled, and training data.
result Stopping methods using unlabeled data are more effective.
New test ensures quality of shared data in machine learning.
problem Ensuring quality of external data in machine learning tasks.
method Distribution-free two-sample testing procedures grounded in conformal outlier detection.
result Identifies valuable external data agents for model personalization.
Paper creates fair synthetic data ensuring equal predictions across sensitive attributes.
problem Ensuring fair predictions across sensitive attributes in synthetic data.
method Equalizing target probability distributions across sensitive attributes in synthetic data generation.
result Synthetic data provides strong fair predictions, equal across all thresholds.
A new method classifies multiple correlated data streams simultaneously.
problem Classifying multiple correlated data streams in practical scenarios.
method Double-Coupling Support Vector Machines (DC-SVM) considers both internal and external correlations.
result The proposed method outperforms traditional methods on artificial and real-world data streams.