An asset network systemic risk (ANWSER) model is presented to investigate the impact of how shadow banks are intermingled in a financial system on the severity of financial contagion. Particularly, the focus of this study is the impact of the following three representative topologies of an interbank loan network betwee…
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48 results for “shadow banking”
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a lar…
Haircutting Non-cash Collateralq-fin.PR
Develops a haircut model for non-cash collateral.
problem Addressing the need for accurate non-cash collateral valuation in shadow banking and OTC derivatives markets.
method Expands haircut definitions, uses a double-exponential jump-diffusion model, and solves for credit risk measurements.
result Computational results show potential for collateral agreements and regulatory capital calculations.
Long-term debt instruments can't be deposit substitutes due to mismatched features.
problem Long-term debt instruments cannot function as deposit substitutes due to their maturity and capital preservation.
method Applied fundamental theory of bond values to 'PEACe Bonds' to show incompatibility.
result Long-term debt instruments cannot be deposit substitutes due to their mismatched features.
New invariants for singular knots and links defined using shadow structures.
problem Defining invariants for singular knots and links.
method Introducing action of singquandles on sets and defining shadow counting and polynomial invariants.
result Enhanced shadow counting invariant for singular knots and links.
HSBC grew from Hong Kong to global dominance despite political upheavals.
problem Surviving and growing in hostile political environments.
method Inorganic growth, leveraging deregulation, and strategic acquisitions.
result HSBC became a global banking behemoth despite political challenges.
The special shadow-complexity of math.GT
Special shadow-complexity equals k+1 for k copies of S1×S3.
problem Calculating the special shadow-complexity of a specific 4-manifold.
method Defined by Costantino using Turaev's shadows, proved for connected sums of S1×S3.
result The special shadow-complexity of k copies of S1×S3 is k+1.
New invariant measures complexity of 2-knots in 4D space.
problem Measuring complexity of 2-knots in 4D space.
method Introduced shadow-complexity based on Turaev shadows.
result Characterized 2-knots with shadow-complexity up to 1.
A shadow diagram is a knot diagram with under-over information omitted; a shadow movie is a sequence of shadow diagrams related by shadow Reidemeister moves. We show that not every shadow movie arises as the shadow of a Reidemeister movie, meaning a sequence of classical knot diagrams related by classical Reidemeister …
Paper studies knotoid chirality using shadow quandle colorings and invariants.
problem Distinguishing knotoids from their mirrors.
method Shadow quandle colorings and cocycle invariants.
result Knotoid is shown to be chiral.
Every shadow can be a knot or a connected sum of trefoils.
problem Understanding the structure of shadows and their relation to knots.
method Analyzing reduced shadows and their relationship to specific knots.
result Every shadow corresponds to a torus knot, twist knot, or connected sum of trefoils.
The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a compact metric space X has the aver- age shadowing property, then every point x…
Almost Perfect Shadow Pricesq-fin.PM
Paper optimizes trading strategies by creating shadow prices for markets with transaction costs.
problem Optimizing trading strategies in markets with transaction costs.
method Developed shadow prices to simplify optimization into a frictionless market, considering second-order transaction costs.
result Alternative strategies outperform shadow prices for risk aversion different from one.
We construct elements of the third quandle homology groups of knot quandles, which are called the shadow fundamental classes. They play the same roles for the shadow quandle cocycle invariants of knots as the fundamental classes of knot quandles does for the quandle cocycle invariants. As an application of the shadow f…
The paper constructs corks and exotic 4-manifolds with controlled shadow-complexity.
problem Constructing exotic 4-manifolds with controlled shadow-complexity.
method Using corks of Mazur type, the authors construct exotic pairs of 4-manifolds with controlled shadow-complexity.
result An infinite family of exotic pairs of 4-manifolds with controlled shadow-complexity.
Computes Kauffman bracket polynomial for specific 2-tangle shadows.
problem Calculating Kauffman bracket polynomial for complex tangle structures.
method Computed Kauffman bracket polynomial for specific 2-tangle shadows with up to 4 crossings.
result Computed polynomial for specific 2-tangle shadows.
The paper presents fundamental groups of complements of shadows in 4-balls.
problem Understanding fundamental groups of 4-manifold complements.
method Similar to Wirtinger presentation, focusing on contractible shadows.
result A presentation of fundamental groups of subpolyhedra in 4-balls.
Shadow biquandles and local biquandles have similar homology and invariants.
problem Comparing homology and invariants of shadow biquandles and local biquandles.
method Defined local biquandle structure on a shadow biquandle and showed isomorphic (co)homology groups and invariant equivalence.
result Homology and invariants of shadow biquandles and local biquandles are equivalent.
Study on inflection points of plane curve shadows with fixed embedded shapes.
problem Minimum number of inflection points in plane curves with fixed embedded shadows.
method Finite coorientation problem on building polygons, dynamic programming, universal lower bound, tree-necklace shadows.
result Exact formula for minimum number of normalized inflections for tree-like shadows.
Proves condition for 4-manifolds with sphere boundary to be standard.
problem Determining when acyclic 4-manifolds with sphere boundary are standard.
method Uses Turaev's shadows to provide a sufficient condition for diffeomorphism to the standard 4-ball.
result If a compact, smooth, acyclic 4-manifold with sphere boundary has shadow-complexity at most 2, it is diffeomorphic to the standard 4-ball.
Method constructs shadowed polyhedra from divides, linking them to Lefschetz fibrations.
problem Linking divides to Lefschetz fibrations.
method Constructing shadowed polyhedra from divides and showing they satisfy the LF-property.
result Links of certain free divides are fibered with positive monodromy.
We introduce an associative algebra Z[X,S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations of Z[X,S] known as shadow modules. We provide examples which demonstrate that the shadow module enhanced invariants are not determined by th…
New forms generalize Whitney forms with rational coefficients for numerical analysis.
problem Numerical problems with singularities near simplex faces.
method Introduce shadow forms and degrees of freedom for integration over faces of blow-up simplices.
result Obtain isomorphism between shadow forms cohomology and cellular cohomology of blow-up simplices.
Study of quandle coloring quivers with dihedral quandles.
problem Link invariants and their enhancements using quandles.
method Introduced shadow quandle coloring quivers and cocycle quivers, studied equivalence with quandle coloring numbers and shadow quandle cocycle invariants.
result Equivalence of quandle coloring quivers with quandle coloring numbers and shadow quandle cocycle quivers with shadow quandle cocycle invariants for specific dihedral quandles.
We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with -structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-…
In this paper we find infinitely many Mazur type manifolds and corks with shadow complexity one among the 4-manifolds constructed from contractible special polyhedra having one true vertex by using the notion of Turaev's shadow. We also find such manifolds among 4-manifolds constructed from Bing's house. Our manifolds …
Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
problem Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
method Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
result Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
The paper studies dynamical properties in semigroups modulo ideals.
problem Analyzing shadowing, expansivity, and stability in semigroups with ideals.
method Investigates shadowing, expansivity, and stability properties in uniform transformation semigroups modulo an ideal.
result Establishes that if a semigroup exhibits shadowing and expansivity modulo an ideal, it is also topologically stable modulo that ideal.
The Link Smoothing Gamemath.CO
We introduce a topological combinatorial game called the Link Smoothing Game. The game is played on the shadow of a link diagram and legal moves consist of smoothing precrossings. One player's goal is to keep the diagram connected while the other player's goal is to disconnect the shadow. We make significant progress t…
For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a "shadow price", i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even i…
We give a self-contained introduction to the theory of Turaev's shadows as a tool to study 3 and 4-manifolds. The goal of the present paper twofold: on one side it is intended to be a shortcut to a basic use of the theory of shadows, on the other side it gives a sketchy overview of some of the recent results on shadows…
A rack shadow is a set X with a rack action by a rack R, analogous to a vector space over a field. We use shadow colorings of classical link diagrams to define enhanced rack counting invariants and show that the enhanced invariants are stronger than unenhanced counting invariants.
This paper compares classical shadows and direct quantum measurement for efficient information extraction.
problem Efficiently extracting classical information from quantum states with limited classical post-processing.
method Quantitative resource analysis comparing classical shadows and direct quantum measurement.
result An efficiency frontier between classical shadows and direct quantum measurement is identified.
Study verifies asymptotic expansion for Reshetikhin-Turaev invariants of fundamental shadow link pairs.
problem Verifying the asymptotic expansion conjecture for Reshetikhin-Turaev invariants of fundamental shadow link pairs.
method Using logarithmic holonomies of meridians and hyperbolic cone structures, the study verifies the conjecture for pairs where is homeomorphic to a fundamental shadow link complement.
result The asymptotic expansion conjecture is true for pairs with sufficiently small cone angles and homeomorphic to a fundamental shadow link complement.
We define a subset of an almost complex manifold (M,J) to be a holomorphic shadow if it is the image of a J-holomorphic map from a compact complex manifold. Notice that a J-holomorphic curve is a holomorphic shadow, and so is a complex subvariety of a compact complex manifold. We show that under some conditions on an a…
Quantile regression attacks outperform shadow models in unseen class membership inference attacks.
problem Failure of shadow model attacks on unseen classes due to limited data access.
method Quantile regression attacks that learn features of member examples.
result Quantile regression attacks achieve up to 11x higher TPR than shadow model-based approaches.
We introduce an algebra Z[X,S] associated to a pair (X,S) of a virtual birack X and X-shadow S. We use modules over Z[X,S] to define enhancements of the virtual birack shadow counting invariant, extending the birack shadow module invariants to virtual case. We repeat this construction for the twisted virtual case. As a…
We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces. We deduce a classification of all 4-manifolds with finite fundamental group and …
Study on links formed by pseudocircle arrangements, focusing on three unavoidable cases.
problem Counting non-equivalent positive oriented links with pseudocircle arrangements as shadows.
method Analyzing three unavoidable arrangements of pseudocircles to estimate the number of non-equivalent links.
result Sharp estimates on the number of non-equivalent positive oriented links for the three unavoidable arrangements.
To any utility maximization problem under transaction costs one can assign a frictionless model with a price process , lying in the bid/ask price interval . Such process is called a \emph{shadow price} if it provides the same optimal utility value as in the original model with bid-as…
Neural Shadow-Mapping uncovers causal links in dynamic systems.
problem Discovering causal structures in dynamic systems with mirage correlations.
method Neural network based method embedding high-dimensional data into a shadow representation for causal link estimation.
result Demonstrates performance in discovering causal links from video-representations of dynamic systems.
The paper introduces a new complexity measure for 4-manifolds and connects it to the trisection genus.
problem Defining and analyzing a new complexity measure for 4-manifolds.
method Defining a new complexity measure and proving an inequality involving the trisection genus.
result Proves an inequality relating the trisection genus to the new complexity measure.
A shadow price is a process lying within the bid/ask prices of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with this price process leads to the same maximal utility as in the original market with transaction costs. For finite probabilit…
Geometric proof confirms link volume conjecture.
problem Volume conjecture for hyperbolic 3-manifolds.
method Topological and skein theoretic techniques.
result Complements of octahedral fully augmented links are isometric to fundamental shadow links.
Researchers derived Kauffman bracket polynomial for Celtic link shadows using two methods.
problem Calculating the Kauffman bracket polynomial for Celtic link shadows.
method Two complementary approaches: recursive relation and 4-tangle algebra.
result Derived Kauffman bracket polynomial for shadows.
Study exact Lagrangian cobordisms in cotangent bundles, proving bounds on sheaf interleaving distance and shadow distance.
problem Understanding Lagrangian cobordisms and their properties in cotangent bundles.
method Use microlocal theory of sheaves, sheaf quantization, and cone decompositions.
result Interleaving distance of sheaves is bounded by the shadow distance of the cobordism.
Turaev's shadow formula calculates the SU(2)-Reshetikhin-Turaev-Witten invariants using shadows, and its expression is somehow similar to a Euler characteristic. We give a short proof of this formula using skein theory. The formula applies to pairs (M,G) where M is a closed oriented 3-manifold and GcM is a (possibly em…
Quandle cocycle invariants form a powerful and well developed tool in knot theory. This paper treats their variations - namely, positive and twisted quandle cocycle invariants, and shadow invariants. We interpret the former as particular cases of the latter. As an application, several constructions from the shadow worl…