Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
AGCA approximates angular variation on the unit sphere, reducing extremal dependence problems to eigenanalysis.
problem Approximating angular variation in multivariate extremes.
method Anchored geodesic component analysis (AGCA) approximates angular variation by great subspheres constrained to pass through a chosen reference direction.
result AGCA finds concentrated tail directions in daily equity-portfolio losses, explaining about 91% of anchored variation.
Study improves portfolio risk estimation methods using robust covariance and CVaR constraints.
problem Improving portfolio risk estimation in the presence of financial data noise and extreme market conditions.
method Exploration of robust covariance estimators, application of CVaR constraints, use of K-means clustering in optimization.
result Robust covariance estimators can outperform market-weighted benchmarks, especially during bull markets.
The paper uses LSMC to price capped American options with time-dependent caps.
problem Pricing American options with time-capped features.
method Least Squares Monte Carlo (LSMC) method.
result The LSMC method converges to the true price as discretization step and number of trajectories approach limits.
It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap (u,uv,v^2) has non-trivial isometric deformations with infinite dimensional freedom. …
Study symmetry of cross-cap surfaces with folding maps.
problem Reflectional symmetry of cross-cap surfaces.
method Characterization of singularities in folding maps.
result Characterized generic singularities on cross-cap.
A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new appro…
Paper classifies symmetries of cross caps using invariants.
problem Classifying symmetries of cross caps.
method Used Bruce-West's normal form and associated functions to create invariants.
result Classified possible symmetries on cross caps.
This paper proves geodesic curvature measures are bounded for curves near cross cap singularities.
problem Boundedness of geodesic curvature measures near cross cap singularities.
method Analyzes intrinsic cross cap singularities and extends Gauss-Bonnet formula.
result Proves boundedness of geodesic curvature measures for curves near cross cap singularities.
Two cross caps in Euclidean 3-space are said to be formally isometric if their Taylor expansions of the first fundamental forms coincide by taking a suitable local coordinate system. For a given C∞ cross cap f, we give a method to find all cross caps which are formally isometric to f. As an application, w…
This research improves value-at-risk estimation during financial crises using non-extensive statistical methods.
problem Underestimation of value-at-risk during financial crises.
method Non-extensive value-at-risk model based on Tsallis entropy and q-Gaussian probability density function.
result The q-Gaussian model provides better value-at-risk estimation during financial crises.
We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we prove that generalized convex caps with the fixed boundary are globally rigid, that…
This study improves mid-cap equity performance with a data-driven, market-neutral approach.
problem Lack of effective strategies for mid-cap stocks.
method Customized long-short equity approach using financial indicators.
result Significant Sharpe ratio of 2.132 in test data.
3D spherical caps are rigid under certain perturbations.
problem Rigidity of 3D spherical caps under specific perturbations.
method Gromov's μ-bubble technique
result 3D spherical caps are rigid under perturbations that maintain metric, scalar curvature, and mean curvature.
Improved LDA with capped l_{2,1}-norm reduces outlier sensitivity.
problem Outliers and noise sensitivity in classical LDA.
method Introducing capped l_{2,1}-norm and proposing CLDA.
result CLDA effectively removes outliers and suppresses noise.
In the paper we consider the following conjecture: if a finite group G possesses a solvable π-Hall subgroup H, then there exist elements x,y,z,t∈G such that the identity H∩Hx∩Hy∩Hz∩Ht=Oπ(G) holds. The minimal counter example is shown to be an almost simple group of Lie type.
Study analyzes order transitions in high, medium, and low market cap stocks using Markov chains.
problem Understanding order transitions in stocks of different market caps.
method First-order discrete-time Markov chain model applied to NASDAQ100 stocks.
result Limit orders exhibit higher inertia during opening hours but decrease in subsequent hours, while market orders increase.
Study of free boundary minimal Möbius bands in spherical caps.
problem Characterizing minimal surfaces with free boundary in spherical caps.
method Analyzing spectral properties and geometric constraints.
result Proves that any free boundary minimal Möbius band in spherical caps must be intrinsically rotationally symmetric.
Proposes a diagnostic method to evaluate factor models using cap-axis integrals.
problem Improving factor model evaluation in low-dimensional spaces.
method Lifts pricing errors into a bridge-alpha curve along the market-capitalization rank axis.
result The cap-axis norm is distinct from Sharpe gain and size exposure.
Proposes a diagnostic method to evaluate factor models using cap-axis integrals.
problem Improving factor model evaluation for low-dimensional models.
method Lifts pricing errors into a bridge-alpha curve along the market-capitalization rank axis.
result The cap-axis norm is distinct from Sharpe gain and size exposure.
Researchers extend CCVaR to multivariate data using Archimedean copulas.
problem No multivariate extension for CCVaR when dependence is given by Archimedean copulas.
method Derive an almost closed-form expression for CCVaR under an Archimedean copula, examine coherence conditions, and conduct numerical experiments.
result An almost closed-form expression for CCVaR under an Archimedean copula is derived.
We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…
Let M be a smooth closed 4k-manifold whose Yamabe invariant Y(M) is nonpositive. We show that Y(M♯lHPk♯mHPkˉ)=Y(M), where l,m are nonnegative integers, and HPk is the quaternionic projective space. When k=4, we also have $$Y(M\sharp l CaP^2\sharp m \bar{CaP^2})=Y(M),…
This paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time, making extensive use of probabilistic arguments and local time, we show that the…
The paper uses Floer homology to study twist coefficients and their behavior after capping off.
problem Behavior of twist coefficients after capping off a boundary component.
method Heegaard Floer homology to constrain twist coefficients.
result Results about fractional Dehn twists and Floer homology of cyclic branched covers.
We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.
CAP adapts optimization to class attributes for better fairness.
problem Heterogeneities across classes impede classification performance.
method CAP generates class-specific learning strategies based on attributes.
result CAP improves over naive approach and is competitive with prior art.
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
Study risk sharing with Lambda VaR under diverse beliefs.
problem Risk sharing among agents with different beliefs.
method Use Lambda Value-at-Risk as preference, analyze under heterogeneous beliefs.
result Explicit formulas for risk sharing under various belief scenarios.
Investors face constraints in Heston's model; optimal allocation differs from naive capped strategy.
problem Optimizing portfolio allocation with convex constraints in Heston's stochastic volatility model.
method Applied duality methods to derive a closed-form solution.
result The optimal constrained portfolio allocation differs from the naive capped portfolio, leading to different wealth outcomes.
Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.
problem Optimizing portfolios with a new risk measure under known or uncertain distributions.
method Existence results for mean-risk optimal portfolios under different distributional assumptions.
result Portfolio selection under Recovery Average Value at Risk provides better control over liabilities.
Paper compares LSTM and GARCH for estimating value-at-risk.
problem Estimating value-at-risk on time series with heteroscedastic dynamics.
method Uses LSTM neural networks to estimate value-at-risk compared to GARCH benchmarks.
result LSTM outperforms GARCH on real market data in terms of exception rate and mean quantile score.
The paper studies parallel surfaces of cuspidal cross caps and their degeneracy.
problem Investigating the geometry and singularities of parallel surfaces of cuspidal cross caps.
method Established a criterion for the degeneracy of the distance squared function using geometric invariants.
result Parallel surfaces degenerate into a degenerated cuspidal S1 singularity at specific distances.
Approximate Incremental Value-at-Risk formulae provide an easy-to-use preliminary guideline for risk allocation. Both the cases of risk adding and risk pooling are examined and beta-based formulae achieved. Results highlight how much the conditions for adding new risky positions are stronger than those required for ris…
Improved multilevel scheme for value-at-risk computation.
problem Discontinuity in Heaviside function affects value-at-risk computation.
method Adaptive multilevel stochastic approximation to mitigate discontinuity.
result Best complexity improved to O(ε−2∣lnε∣25). New method distinguishes 4-manifold types using trisections.
problem Distinguishing different 4-manifold types.
method Capping operation to transform relative trisections into closed 4-manifold diagrams.
result Examples of non-diffeomorphic relative trisections of the same 4-manifold.
Value-at-Risk is a flawed substitute for non-ruin capital, leading to misleading financial standards.
problem Misuse of Value-at-Risk as a risk measure, replacing non-ruin capital, leads to flawed financial standards.
method Mathematical analysis of risk measures and their implications on financial standards.
result Non-ruin capital is a more accurate risk measure than Value-at-Risk, necessitating its adoption over the former.
We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots.
Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
The paper analyzes how to combine self-protection and self-insurance for risk reduction.
problem Combining self-protection and self-insurance for risk reduction when market insurance is absent.
method The approach uses Value-at-Risk and Tail Value-at-Risk to evaluate residual risk and solves the problem using isoquant geometry based on marginal-balance curves.
result The analysis identifies the conditions under which self-protection and self-insurance behave as substitutes or complements.
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new θ-index based on equal level relationships between Value at Risk and Expected Shortfall. result The θ-index provides a level-dependent, scale-free measure of upper tail behavior. FSD-CAP improves graph feature imputation under high missing rates.
problem Challenges in imputing missing node features in graphs, especially under high missing rates.
method Two-stage framework: subgraph expansion, fractional diffusion, class-aware propagation.
result Significantly improved imputation quality compared to existing methods, achieving high accuracy on benchmark datasets.
We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.
The study finds the optimal metrics for free boundary minimal surfaces in spherical caps.
problem Optimizing metrics for free boundary minimal surfaces in spherical caps.
method Introducing functionals based on eigenvalues of Steklov-type problems and proving maximizers are induced by immersions.
result Maximizing metrics are induced by free boundary minimal immersions in geodesic balls of a round sphere.
A new framework for robust risk measurement and portfolio optimization.
problem Uncertainty in mean-covariance space and portfolio optimization challenges.
method Modeling uncertainty with Gelbrich distance and prior structural information, related to optimal transport theory.
result Mean-covariance robust portfolio optimization simplifies to Markowitz model with a regularization term.
Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating wors…
Let (G,h) be a nilpotent Lie group endowed with a left invariant Riemannian metric, g its Euclidean Lie algebra and Z(g) the center of g. By using an orthonormal basis adapted to the splitting $\mathfrak{g}=(Z(\mathfrak{g})\cap[\mathfrak{g},\mathfrak{g}])\oplus O^+\oplus (Z(\mat…
CAP algorithm controls FCR in online selective prediction.
problem Online predictive tasks with temporal multiplicity and FCR control.
method CAP framework with adaptive pick rule and calibration set construction.
result CAP achieves exact selection-conditional coverage guarantee and FCR control.