Modeling market impacts leads to perfect hedging strategies.
problem Trading with permanent market impacts and nonlinearity.
method Modeling market impacts using g-expectation and nonlinear stochastic integrals; introducing completeness condition for perfect replication.
result Under certain conditions, derivatives can be perfectly hedged dynamically.
Perfect hedging strategies found in rough Heston models.
problem Managing risks of derivatives under rough volatility models.
method Explicit hedging strategies using the underlying asset and forward variance curve.
result Theoretical perfect hedging (at least) in rough Heston models.
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A general expansion theory is de…
We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient co…
Financial markets have developed a lot of strategies to control risks induced by market fluctuations. Mathematics has emerged as the leading discipline to address fundamental questions in finance as asset pricing model and hedging strategies. History began with the paradigm of zero-risk introduced by Black & Scholes st…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual notion of arbitrage. Several examples illustrate the non probabilistic arbitrag…
New algorithm ensures consistent results in constrained MAB problems.
problem Achieving consistent results in constrained MAB problems.
method Developed replicable algorithms for constrained MAB problems using the optimism principle.
result Regret and constraint violation of replicable algorithms match those of non-replicable ones.
Unified framework for fixed-income pricing and liability replication.
problem Static arbitrage and discount curve construction.
method Model-free framework for static fixed-income pricing and liability replication.
result Existence of strictly positive discount curves reproducing market prices and least-cost super-replicating portfolios.
New study on replicability and stability in machine learning algorithms.
problem Ensuring consistent results in machine learning models without fixing randomness.
method Introduced global stability and list replicability concepts, proving their equivalence and boosting list replicability.
result Global stability can only be achieved weakly, while list replicability can be boosted to achieve high probability of consistent results.
Characterizes super-replication prices in a financial market model.
problem Characterizing prices in a financial market model.
method Characterizes prices as the supremum of mono-prior super-replication prices through extreme priors and martingale measures.
result Super-replication prices are the supremum of mono-prior super-replication prices.
Study on computational aspects of replicable learning, bridging statistical and algorithmic perspectives.
problem Understanding the computational connections between replicability and various learning paradigms.
method Design of replicable learners, lifting framework, and transformation techniques.
result Efficient replicable learners for specific learning problems under various distributions.
The paper classifies self-replicating 3D shapes using algebraic models.
problem Understanding self-replicating 3D shapes.
method Using idempotents in the (2+1)-cobordism category to classify 3-manifolds.
result A classification theorem for self-replicating 3-manifolds.
New set type with no uniformly perfect subsets.
problem Understanding compact sets without uniformly perfect subsets.
method Introduced hereditarily non uniformly perfect sets and compared them with other types of sets.
result Example of a compact set with Hausdorff dimension 2 and positive logarithmic capacity is hereditarily non uniformly perfect.
Study shows high costs for replicating financial claims with fixed fees.
problem High costs for replicating financial claims in markets with fixed transaction costs.
method Stochastic impulse control problem with terminal state constraint.
result Super--replication prices are prohibitively costly and lead to trivial strategies in continuous models.
New algorithm prevents strategic replication in multi-armed bandit problems.
problem Strategic replication by agents can exploit bandit algorithms' balance.
method Designs Hierarchical UCB (H-UCB) and Robust Hierarchical UCB (RH-UCB) algorithms.
result Achieves O(lnT)-regret and sublinear regret in realistic scenarios. Extends super-replication theorem with dynamic strategies and transaction costs.
problem Dynamic super-replication under proportional transaction costs.
method Generalizes admissible strategies and defines a well-defined super-replication price process.
result Well-defined super-replication price process in dynamic setting.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
Study reveals statistical bias in dataset replication, reducing accuracy drop from 11-14% to 3.6%.
problem Statistical bias in dataset replication affects model generalization accuracy.
method Analyzed ImageNet-v2, identified and corrected for bias, and compared results.
result Correcting bias reduces accuracy drop from 11-14% to 3.6%.
Study replicability in high-dimensional statistics, resolving open problems.
problem Ensuring consistent results in high-dimensional statistical tasks.
method Introduced replicable learning algorithms and established computational and statistical equivalence with high-dimensional isoperimetric tilings.
result Matching sample complexity upper and lower bounds for replicable mean estimation and coin problem.
New uniformity tester ensures consistent results across different samples.
problem Non-replicable behavior of uniformity testing algorithms.
method Develops a replicable uniformity tester with improved sample complexity.
result Achieves nearly linear dependence on replicability factor ρ. Paper proposes a new method to detect node replication attacks in Vehicular Ad-hoc Networks.
problem Node replication attacks in Vehicular Ad-hoc Networks.
method Adapted statistical methodology for detecting node replication attacks.
result New method outperforms state-of-the-art techniques in detecting node replication attacks.
In his seminal 1951 paper "Extreme forms" Coxeter \cite{cox51} observed that for n≥9 one can add vectors to the perfect lattice $\sfA_9$ so that the resulting perfect lattice, called $\sfA_9^2$ by Coxeter, has exactly the same set of minimal vectors. An inhomogeneous analog of the notion of perfect lattice is tha…
ERICA assesses replicability of cluster analysis results.
problem Lack of quantitative scrutiny for clustering results.
method ERICA: a framework to assess replicability of cluster analysis.
result Clusters are found to be replicable in synthetic data but not in real-world datasets.
The study examines properties of perfect fluid spacetimes in Einstein's theory.
problem Analyzing curvature properties of perfect fluid spacetimes.
method Assuming perfect fluid as the source, the paper investigates solutions to Einstein's field equations.
result Properties of perfect fluid spacetimes are explored in the context of Einstein's theory.
The paper studies Ricci solitons in perfect fluid spacetimes with specific vector fields.
problem Analyzing Ricci solitons in perfect fluid spacetimes with torse-forming vector fields.
method Examined perfect fluid spacetimes with torse-forming vector fields ξ, determined Ricci solitons, and classified their behavior as expanding, steady, or shrinking.
result Conditions for the behavior of Ricci solitons in these spacetimes were identified.
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the super-replication price. We provide two families of fully incomplete models: stochast…
Algorithm decides if pseudo-Anosov flows have perfect fits.
problem Determining if pseudo-Anosov flows have specific asymptotic properties.
method Algorithm based on box decompositions and universal cover analysis.
result Algorithmic decision on pseudo-Anosov flows' perfect fit status.
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential …
Paper introduces ρ-Perfect to estimate model-human correlation in subjective datasets.
problem Inherent noise in subjective ratings limits model-human correlation quantification.
method Defines ρ-Perfect as highest achievable correlation between perfect predictor and human ratings. Estimates based on heteroscedastic noise scenarios. result Demonstrates ρ-Perfect can distinguish model limitations from data quality issues. The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case o…
Paper proves almost all Gaussian graphical models are perfect.
problem Determining when Gaussian graphical models are perfect.
method Direct approach to Gaussian graphical models, extending Lněnička and Matúš's construction.
result Almost all Gaussian graphical models are perfect.
New approach optimizes expensive black-box systems with uncertain outputs.
problem Optimizing expensive black-box systems with limited data and uncertainty.
method Flexible non-interpolating surrogate model (TK-MARS) and Smart-Replication approach.
result TK-MARS outperforms original MARS and detects important variables.
New cohomology theory for planar graphs with perfect matchings.
problem Understanding cohomology of planar trivalent graphs with perfect matchings.
method Introducing a cohomology theory and defining new polynomials.
result 2-factor polynomial can indicate 4-face colorability.
Researchers study solitons in perfect fluid spacetime geometry.
problem Exploring solitons in perfect fluid spacetime geometry.
method Analyzing curvature tensors and determining η-Ricci and η-Einstein solitons. result Conditions for solitons to be steady, expanding, or shrinking are derived.
New conditions for GRW space-times to be perfect-fluid space-times.
problem Conditions for GRW space-times to be perfect-fluid.
method Gray's decomposition of the gradient of the Ricci tensor, determining Ricci tensor forms in invariant subspaces.
result For most GRW space-times, the Ricci tensor is Einstein or perfect fluid.
Adaptive replication improves stochastic function optimization.
problem Challenges in accurately estimating functions with high variance.
method Trust-region-based Bayesian optimization with adaptive replication.
result Adaptive replication substantially improves solution accuracy and efficiency.
Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.
problem Designing clustering algorithms that produce the same partition on repeated runs under the same distribution.
method Utilizing approximation routines for combinatorial clustering problems in a black-box manner.
result Replicable algorithms for statistical k-medians, k-means, and k-centers with specified approximation and sample complexities. Study on static perfect fluid space-time geometry and boundary estimates.
problem Investigate the geometry and boundary properties of static perfect fluid space-time.
method Used generalized Reilly's formula to establish geometric inequalities and boundary estimates.
result Obtained new boundary estimates involving the Brown-York mass and first eigenvalue of the Jacobi operator.
Investment strategies for rank-dependent utility agents are derived in a continuous-time market.
problem Time inconsistency in rank-dependent utility models.
method Study of consistent planners seeking intra-personal equilibrium strategies.
result Explicit final wealth profile replicating equilibrium strategies, with scaling function derived.
The paper examines uniform perfectness of diffeomorphism groups on open manifolds.
problem Uniform perfectness of diffeomorphism groups on open manifolds.
method Study of uniform perfectness, boundedness, and simplicity of diffeomorphism groups of compact and open manifolds.
result Obtained upper bounds of diameters for commutator length, balls, and conjugation-generated norm.
In this paper we propose a new robust algorithm to find the optimal static replicating portfolios for general nonlinear payoff functions and give the estimate of the rate of convergence that is absent in the literature. We choose the static replication by minimizing the error bound between the nonlinear payoff function…
TF-Replicator simplifies distributed ML for researchers.
problem Complex distributed ML code for researchers.
method Abstraction over TensorFlow, data-parallel and model-parallel.
result Strong scalability without distributed systems expertise.
Uniformly perfect Morse boundaries characterize geometric properties of groups.
problem Characterizing geometric properties of groups using Morse boundaries.
method Introducing and geometrically characterizing uniformly perfect Morse boundaries for proper geodesic metric spaces.
result The Morse boundary of any finitely generated, non-elementary group is uniformly perfect if it is nonempty.
Study mapping class groups of infinite type surfaces with noncompact boundaries.
problem Classify pure mapping class groups of infinite type surfaces.
method Developed a method to cut surfaces into simpler ones and combined recent results.
result Complete classification of perfect and uniformly perfect pure mapping class groups.
Unified valuation theory for credit risk, defaults, and funding costs.
problem Valuation under credit risk, defaults, and funding costs.
method Unified valuation theory expanding replication approach to incorporate credit risk, defaults, and funding costs.
result Clarifies the relationship between the adjusted cash flows approach and the replication approach.
The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading independence from the structure of the graph (e.g., Pearl, 1988; Lauritzen, Dawid, La…
The paper prices long-term options with a reflecting barrier model.
problem Pricing long-term options with asset price limits.
method Model asset price as geometric Brownian motion with a lower reflecting barrier, pricing options using compound options.
result Option prices can be determined using standard risk-neutral arguments, and hedging strategies are available.