The study allocates income based on journal impact and coauthorship contributions.
problem Inequitable income distribution among co-authors of research papers.
method Uses journal impact factor and coauthorship contribution, applying Cantor's theory and Harmonic Credit Index.
result Develops a model for fair income distribution among authors.
A new model uses a Levy-driven process to value credit index swaptions.
problem Valuation of credit index swaptions in financial markets.
method Proposes a Levy-driven Ornstein-Uhlenbeck process to model risk-free rate and default intensities.
result Derives formulas for characteristic function, moments, and stationary distribution.
Optimizes credit index option hedging with reinforcement learning.
problem Finding the best strategy for hedging credit index options.
method Applied reinforcement learning with TRVO algorithm in a realistic setting.
result The derived hedging strategy outperforms traditional methods.
Paper proposes a framework for precise daily default risk prediction of Chinese credit bonds.
problem Inadequate and inaccurate bond information disclosure creates risk of default for investors.
method Framework includes summarizing factors impacting defaults, constructing a risk index system, and using ConvLSTM neural network for prediction.
result The model provides more responsive and accurate daily default risk predictions than authoritative ratings.
Develops a three-currency HJM framework for Brazilian credit markets, finding significant credit spread differences between indexed segments.
problem Identifies and quantifies differences in corporate credit spreads between two parallel segments of the Brazilian bond market.
method Uses a Heath-Jarrow-Morton framework to model corporate credit as a separate economy, linking it to nominal and real economies through synthetic rates.
result Empirically finds a 640 basis point average difference in credit spreads between CDI-indexed and IPCA-indexed segments, stable through market cycles.
Low-index harmonic maps from S3 to S2 are simple.
problem Characterizing harmonic maps with low Morse index.
method Proving any such map is an isometry, fibration, and holomorphic composition.
result Harmonic maps of low index are restricted to specific compositions.
We present a new model for credit index derivatives, in the top-down approach. This model has a dynamic loss intensity process with volatility and jumps and can include counterparty risk. It handles CDS, CDO tranches, Nth-to-default and index swaptions. Using properties of affine models, we derive closed formulas for t…
Study bounds the Morse index of a special torus to 1.
problem Bounding the Morse index of a conformal harmonic torus.
method Min-max construction with harmonic replacement and conformal harmonic torus.
result The Morse index is bounded by one.
GBST model improves credit risk quantification using survival analysis.
problem Quantifying credit risk in heterogeneous consumer finance data.
method Gradient boosting survival tree (GBST) model integrating survival analysis and gradient boosting.
result GBST model outperforms existing survival models in credit risk quantification.
Paper proves existence of Dirac-harmonic maps with trivial index.
problem Finding Dirac-harmonic maps with trivial index.
method Defining a new quantity and proving its homotopy invariance.
result Existence of Dirac-harmonic maps from closed Riemann surfaces to Kähler manifolds.
Estimates index of harmonic maps from surfaces to complex projective spaces.
problem Estimating the index of harmonic maps from surfaces to complex projective spaces.
method Estimating dimensions of spaces of holomorphic sections of line bundles.
result Improved lower bounds on the index of harmonic maps.
The paper bounds the energy index of harmonic Gauss maps on surfaces.
problem Bounding the energy index of harmonic Gauss maps on surfaces.
method Analyzes closed and complete non-compact surfaces in Lie groups with bi-invariant metrics.
result The energy index of the Gauss map is bounded by the topological genus.
Study finds implicit government guarantee improves municipal investment bond ratings.
problem Questioning the objectivity of municipal investment bond ratings due to implicit government guarantee.
method Text mining of policy documents and PMC index model for implicit guarantee strength calculation.
result Implicit government guarantee boosts municipal investment bond ratings, especially in less developed regions.
Study price impact in OTC credit index market without order book.
problem Estimate price impact in OTC credit index market with no order book.
method Applied propagator technique to classify trades and correct for errors.
result Price impact is mainly permanent in OTC credit index market.
We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the source and target manifolds is a harmonic map.
Study index bounds for harmonic maps sequences with bubbles.
problem Upper and lower bounds of index and nullity for harmonic maps.
method Study limiting behavior of eigenfunctions of linearized operator; diagonalize index form with bilinear form varying with sequence.
result Obtain index bounds and show convergence of eigenfunctions on weak limit, bubbles, and neck regions.
Stability of Morse index for harmonic maps on degenerating surfaces analyzed.
problem Analyzing stability of Morse index for harmonic maps on degenerating Riemann surfaces.
method Analysis of second variation of energy, identification of conditions for upper semicontinuity, explicit contribution of geodesics.
result Sharper control of spectrum of Jacobi operator, explicit contribution of geodesic segments to Morse index.
We call indexed-biharmonic maps, the solutions of a particular non linear elliptic PDE of order 4. This is a generalization of harmonic maps which verifies that biharmonic maps are biharmonic of index 0. The goal of this article is to study submanifolds of Sn whose inclusion is non harmonic and indexed-biha…
AXI assesses bank funding costs transparently, improving loan pricing and reducing financial risk.
problem Lack of credit-sensitive funding benchmarks after LIBOR transition.
method AXI aggregates unsecured funding transactions across maturities, producing a daily credit spread.
result AXI correlates with financial conditions and market stress, reducing funding risk and offering spread discounts.
New algorithms learn multi-index models via harmonic analysis, achieving statistical and computational trade-offs.
problem Learning multi-index models with unknown projections of input data.
method Exploiting the equivariance of the problem under the orthogonal group, we derive lower bounds and construct spectral algorithms based on harmonic tensor unfolding.
result Achieve statistical and computational trade-offs between sample and runtime complexity.
In this note, we investigate estimates of the Morse index for F-harmonic maps into spheres, our results extend partially those obtained in ([14]) and ([15]) for harmonic and p-harmonic maps.
Unified framework connects credit risk metrics with information theory.
problem Disconnection between industry-standard metrics and statistical theory.
method Unified information-theoretic framework, proving IV equals PSI, deriving standard errors, formalizing trade-off, automated binning with XGBoost.
result Unified framework connects IV and PSI, providing statistical foundation for metrics.
Study estimates self-shrinker index with conical ends, proving index bound.
problem Estimating the index of self-shrinkers with asymptotically conical ends.
method Constructing Gaussian Harmonic forms and extending index estimates.
result Proves Morse index of self-shrinkers is at least (2g+r-1)/3.
In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the candidate numeraire one would use to define a pricing measure is n…
Optimal credit and consumption strategies in a switching market with default contagion.
problem Optimal portfolio and consumption decisions in a credit market with default contagion.
method Cobb-Douglas utility, recursive ODE system, backward solution from all-default state.
result Existence and uniqueness of optimal feedback controls, verification theorem.
Study on harmonic maps from surfaces with energy bounds and neck domains.
problem Behavior of harmonic maps with bounded energy on complex domains.
method Analysis of a sequence of harmonic maps in generalized neck domains.
result Upper bound of energy density and study of nullity and index limits.
In this paper we are concerned with harmonic maps and minimal immersions defined on compact Riemannian manifolds and with values in homogenous strongly harmonic manifolds. We show some results on the Morse index by varying these maps along suitable conformal vector fields. We obtain also that they are global maxima on …
Study finds bound on energy of minimal spheres on complex manifolds.
problem Finding bounds on energy of minimal spheres on complex manifolds.
method Proving existence of harmonic spheres with Morse index bound one.
result Sum of energies of minimal spheres realizes a geometric invariant width.
Paper derives second variational formula for statistical manifold mappings.
problem Variational formulas for mappings between statistical manifolds.
method Develops second variational formula for harmonic mappings, defines stability, index, and nullity.
result Shows weakly stability for harmonic mappings into statistical manifolds of non-positive curvature.
Study on harmonic map blow-up behavior with finite index.
problem Blow-up phenomena in harmonic map sequences with finite index.
method Analysis of αk-harmonic map sequences with bounded uniformly αk-energy. result Energy identity holds true for limiting necks of convergence.
Study finds no significant impact of US sovereign credit rating downgrade on equity market.
problem Impact of US sovereign credit rating downgrade on US equity market.
method Event study methodology using three companies and S&P500 index.
result No significant effects of US sovereign credit rating downgrade on US equity market.
Researchers prove an index formula for spinors on 3-manifolds branching along graphs.
problem Index formula for Dirac operators on 3-manifolds with branch points.
method Analyzes Dirac operator on two-valued spinors on a 3-manifold with a graph branch, with boundary conditions.
result Index formula vanishes when the branch is a smooth curve, extends to graphs with vertices.
Study harmonic spinors on a family of Einstein manifolds, including Taub-NUT and Eguchi-Hanson.
problem Existence and explicit solutions of harmonic spinors on Einstein manifolds.
method Solve for spinors harmonic with respect to the Dirac operator twisted by a geometric connection.
result Explicit solutions and agreement with index theorem boundary conditions.
Small hypersphere is unstable in both 4-harmonic and ES-4-harmonic settings.
problem Stability of small hypersphere in 4-harmonic and ES-4-harmonic settings.
method Analysis of normal variations of small hypersphere.
result Normal index of small hypersphere is one in both 4-harmonic and ES-4-harmonic settings.
Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalise harmonic maps. We consider the Hopf map $ψ:\s^3\to \s^2$ and modify it into a nonharmonic biharmonic map $φ:\s^3\to \s^3$. We show φ to be unstable and estimate its biharmonic index and nullity. Resolving the s…
New method uses spherical harmonics to simplify learning single-index models.
problem Learning single-index models with unknown one-dimensional projections.
method Proposes using spherical harmonics instead of Hermite polynomials to capture rotational symmetry.
result Characterizes the complexity of learning single-index models under arbitrary spherically symmetric input distributions.
Paper evaluates different models for predicting credit default swap volatility.
problem Predicting the Implied Volatility of credit default swaps.
method SVM, Gradient Boosting, and Attention-GRU Hybrid model.
result Identifies strengths in classical and SOTA machine learning methods.
Paper calculates virtual dimension of spinor zero loci on 3-manifolds.
problem Computing the virtual dimension of spinor zero loci.
method Uses Kuranishi structure and index theory developed by Bruning, Seeley, and Yang.
result Proves virtual dimension is zero for 3-manifolds.
Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as well as sequences of solutions that have arisen in other physical models. We ap…
Estimates the index of the Laplace operator on planar domains with Robin boundary condition.
problem Index estimates for planar domains with Robin boundary condition
method Combines conformal and spectral techniques with topology of the domain.
result Lower bounds for the index in terms of the number of boundary components.
In this note we investigate the (E)-index and the (E)-nullity of vacuum solutions from the two-torus into the two sphere.
Scattering theory for harmonic one-forms on Riemann surfaces.
problem Understanding harmonic one-forms on Riemann surfaces.
method Constructing scattering theory through boundary value problems and integral operators.
result Explicit expression for the scattering matrix and proof of unitarity.
The paper proves geometric rigidity using harmonic twisted spinors and scalar curvature comparison.
problem Proving geometric rigidity for closed Riemannian spin manifolds with specific properties.
method Using Gromov's exact-lift two-form method and harmonic spinors to analyze scalar curvature.
result The original metric is Einstein, and the universal cover is real hyperbolic in the positive-spectrum case.
Paper analyzes harmonic maps blow-up neck regions.
problem Understanding blow-up regions in harmonic maps.
method Proved refined estimates in neck regions.
result New estimate reveals neck shape and inequality about nullity and index.
J.Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variation formula. In this paper, we give the second variation formula of k-energy, and give a notion of index, nullity and weakly stable. We also study k-harmonic maps into the product Riemannian manifold, and k-harmonic curves…
Aiming at quantifying and evaluating the regional commercial environment along with the level of economic development among cities in mainland China, the concept of China City Commercial Environment Credit Index(CEI) was first introduced and established in 2010. In this manuscript, a historical review and detailed intr…
Study compares CDS databases and finds discrepancies due to various factors.
problem Comparing discrepancies among CDS databases.
method Comparing five major sources of corporate CDS prices over 2004-2010.
result CMA quotes lead price discovery and databases disagree on stock-CDS return analysis.
Constructs biharmonic and r-harmonic submanifolds in cohomogeneity one manifolds.
problem Constructing biharmonic and r-harmonic submanifolds. method Using cohomogeneity one manifolds, the normal index of submanifolds is studied, and new examples are provided.
result Constructs metrics on the sphere with biharmonic non-minimal hypersurfaces.