The paper quantifies when a trading strategy's drawdown becomes a cause for concern.
problem Detecting when a profitable trading strategy starts to degrade over time.
method Quantitative analysis of drawdown length and depth for upward drifting Brownian motions.
result Drawdowns lasting too long or being too deep indicate a need to revise the strategy's Sharpe ratio.
In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, Wt=Bt+μt,t≥0, where (Bt) is a standard Brownian motion. Truncated variation differs from regular variation by neglect…
Study revises results on a specific type of 3D paracontact metric manifolds.
problem Revising results on a specific type of 3D paracontact metric manifolds.
method Analyzing a defined class of 3-dimensional paracontact metric manifolds.
result Revision of previous findings in the field.
A method for selecting pseudo-labeled data in semi-supervised learning using generalized Bayes and soft revision.
problem Selecting pseudo-labeled data for semi-supervised learning with robustness to uncertainty.
method Using credal sets and the Gamma-Maximin method with soft revision to update priors and select pseudo-labeled data.
result The Gamma-Maximin method with soft revision can achieve promising results, especially in scenarios with low labeled data proportions.
Pricing Chinese convertible bonds using Monte Carlo simulation and dynamic programming.
problem Pricing Chinese convertible bonds accurately.
method Monte Carlo simulation and dynamic programming with regression and backward induction.
result An underpriced strategy significantly outperforms benchmarks.
GRCN improves GCNs by predicting missing edges and revising weights.
problem Sub-optimal solutions due to incomplete and noisy real-world graphs.
method Introduces a GCN-based graph revision module for predicting missing edges and revising weights.
result GRCN consistently outperforms strong baseline methods, especially on incomplete graphs.
Upper bounds on revised first Betti number and torus stability for RCD spaces.
problem Bounding the revised first Betti number and stability of RCD spaces.
method Proving an upper bound on the rank of the abelianised revised fundamental group and establishing torus stability.
result Spaces with saturated upper bound on revised first Betti number are mGH-close to flat tori.
Proves existence and uniqueness of hypersurfaces with prescribed curvature in Minkowski space.
problem Prescribed curvature problem for entire hypersurfaces in Minkowski space.
method Analyzes functions and spacelike hypersurfaces to prove existence and uniqueness.
result Existence and uniqueness of entire, strictly convex, spacelike hypersurfaces with prescribed curvature.
Paper calculates perpetual American put option pricing with drawdown event in Lévy market.
problem Pricing perpetual American put options with a drawdown event in a Lévy market.
method Derives explicit price using geometric Lévy process with downward jumps, optimal stopping rule, and martingale arguments.
result Optimal stopping rule is the first time asset price falls below a specific value.
SPLICE simulates incurred losses and their revisions.
problem Simulating incurred losses and their revisions in insurance.
method Continuous time simulation of individual claims with revisions over their lifetime.
result Incorporates dependencies and properties of incurred losses.
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
The percolation model of stock market speculation allows an asymmetry (in the return distribution) leading to fast downward crashes and slow upward recovery. We see more small upturns and more intermediate downturns.
CROQ optimizes LLM decision-making by narrowing down choices and improving accuracy.
problem Uncertainty in LLM outputs poses risks in high-stakes domains.
method Conformal prediction (CP) and optimization (CP-OPT) to minimize prediction set sizes.
result CROQ improves LLM accuracy, especially with CP-OPT.
Revised ct-SNE improves t-SNE for visualizing data beyond labels.
problem ct-SNE fails in realistic settings where data is well clustered over labels.
method Conditioning high-dimensional similarities, storing nearest neighbors separately, and using speedups.
result Improved embedding quality and scalability.
Paper trains models to resist spurious patterns by having humans revise documents.
problem Machine learning models often rely on spurious patterns, leading to poor performance.
method Humans revise documents to retain coherence and avoid unnecessary changes, creating a combined dataset.
result Models trained on combined datasets perform better than those trained on original or manipulated data alone.
A framework for cost of belief revision in uncertain agents.
problem Cost of revising beliefs in uncertain agents.
method Axiomatic framework for transport-based belief costs, postulates P0 and P1.
result Cost metric is conformally reweighted by Fisher information, leading to a cost floor diverging at certainty.
Revised proof shows ribbonness of surface-links in 4-sphere.
problem Determining ribbonness of surface-links in 4-sphere.
method Surgery along fusion 1-handle systems to prove ribbonness.
result Surface-links in 4-sphere are ribbon if certain conditions are met.
Study on RCD(0,N) spaces with small linear diameter growth.
problem Understanding structure properties of RCD(0,N) spaces.
method Analyzing the (revised) fundamental group of RCD(0,N) spaces.
result Proved that the revised fundamental group is finitely generated for RCD(0,N) spaces with small linear diameter growth.
New method identifies uncertainty shocks in financial markets using revised VIX.
problem Traditional VIX fails to capture non-Gaussian, heavy-tailed asset returns.
method Fit a double-subordinated Normal Inverse Gaussian Levy process to S&P 500 option prices to construct a revised VIX.
result Revised VIX provides a more comprehensive measure of volatility reflecting extreme movements and heavy tails.
News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable est…
Two DRL policies collaborate to solve NP-hard routing problems.
problem Solving complex routing problems like TSP without expert knowledge.
method Learning Collaborative Policies (LCP) using seeder and reviser policies.
result Improves solution quality over single-policy DRL on various NP-hard routing problems.
WHAI combines autoencoding and MCMC for scalable topic modeling.
problem Training scalable deep topic models for big corpora.
method Develops a hybrid autoencoding inference network for deep latent Dirichlet allocation.
result WHAI achieves both scalability and speed in topic inference.
Bayesian logistic regression improves clinical risk prediction models over time.
problem Improving clinical risk prediction models after deployment to adapt to temporal shifts.
method Bayesian logistic regression (BLR) and Markov variant (MarBLR) for online recalibration and revision of prediction models.
result BLR and MarBLR consistently outperform static models and other online revision methods, improving average AUC and calibration index.
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which give…
This paper has been withdrawn, because its material has been revised and became part of paper math.GT/0010184
This paper compares AMMs and LOBs in exchange mechanisms, formalizing complexity vs. expressiveness trade-offs.
problem Designing efficient exchange mechanisms between assets.
method Formalizes a complexity-approximation trade-off for CFMMs and LOBs, introducing an exchange complexity measure.
result Optimally expressive mechanisms can be designed with minimal complexity, allowing for arbitrary demand curves.
RoGAT enhances GAT robustness against adversarial attacks.
problem Vulnerability of GAT to adversarial attacks.
method Dynamic adjustment of edge weights and features, with an extra attention score.
result RoGAT outperforms other defensive methods in robustness tests.
Develops a flexible deep autoencoding topic model with scalable hybrid Bayesian inference.
problem Flexible and interpretable document analysis models.
method DATM with hybrid Bayesian inference, including topic-layer-adaptive stochastic gradient Riemannian MCMC and Weibull variational encoder.
result Demonstrates scalability and efficacy on big corpora in unsupervised and supervised learning tasks.
The study finds significant power-law cross correlations in Bitcoin's return-volatility dynamics.
problem Investigating asymmetry in Bitcoin's return-volatility relationships.
method Analysis of daily and high-frequency Bitcoin data to identify cross correlations.
result Power-law cross correlations between returns and future volatilities are observed, indicating long-range dependencies.
Extended CIR process with jumps at fixed dates for modeling overnight rates.
problem Modeling overnight rates with jumps at predetermined dates.
method Formal definition and existence proof of a CIR process with stochastic discontinuities.
result Extended CIR process inherits affine property and non-negativity.
We establish a surgery formula for 3-dimensional Seiberg-Witten monopoles under (+1) Dehn surgery on a knot in a homology 3-sphere. (substantial revision)
This paper has been withdrawn by the authors. Significantly revised versions of the results of this paper are now available in arXiv:0707.0487v2 and arXiv:0808.3169v1.
This paper optimizes liquidity provision in automated market makers using auction theory.
problem Optimizing profit for a monopolist liquidity provider in automated market makers.
method Introduces a Bayesian-like belief inference framework to model AMMs, characterizes profit-maximizing strategies using Myerson's optimal auction theory.
result Characterizes the optimal demand curve and payments for an IC AMM, revealing a bid-ask spread caused by asymmetry and monopoly pricing.
We use the maximum entropy principle for pricing the non-life insurance and recover the Bühlmann results for the economic premium principle. The concept of economic equilibrium is revised in this respect.
Enhances fault tolerance of neural networks for security-critical applications.
problem Fault tolerance of neural networks is biased and can lead to severe consequences in security-critical scenarios.
method Proposes a revised implementation that significantly enhances the fault tolerance property of neural networks with detailed mathematical analysis.
result Significantly increased fault tolerance of neural networks for security-critical applications.
Estimates peeking effects in p-values to correct bias.
problem Data peeking biases reported p-values downward.
method Develops mechanisms to estimate running extrema of test statistics.
result Corrects bias in p-values due to peeking.
This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2
We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions, essentially completely rewritten in places.
This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the fo…
New model describes asset price dynamics during economic bubbles.
problem Modeling asset price dynamics during economic bubbles.
method Introduced a new diffusion process with an exponential decay drift term.
result Calculated the first passage time density for asset price crashes.
We propose a primitive called PJOIN, for "predictive join," which combines and extends the operations JOIN and LINK, which Valiant proposed as the basis of a computational theory of cortex. We show that PJOIN can be implemented in Valiant's model. We also show that, using PJOIN, certain reasonably complex learning and …
Improves SA-CCR model to be more consistent and risk-sensitive.
problem Inconsistent and risk-insensitive SA-CCR model.
method Cashflow decomposition in a 3-Factor Gaussian Market Model.
result Makes SA-CCR self-consistent and risk-sensitive.
Survey article on recent Kähler geometry and exceptional holonomy.
problem Exploring recent advancements in Kähler geometry and exceptional holonomy.
method Not specified in the abstract, likely a review of existing research.
result Not specified in the abstract, likely a summary of recent findings.
Two studies explain high margin loan rates by brokers.
problem High margin loan rates charged by stock brokers.
method Two approaches: finite revisions and monopolistic pricing.
result Small differences in revision frequency or monopoly pricing can explain loan rates.
Proves special alternating knots cannot be decomposed as non-trivial band sums.
problem Understanding the structure and properties of special alternating knots.
method Analyzes concordance properties and uses band sums to restrict knot decompositions.
result Conjecture that special alternating knots are ribbon concordance minimal is verified in many cases.
We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K. Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston equivalent to a rational map.
We construct Bott-type and equivariant Seiberg-Witten Floer homology and cohomology for 3-manifolds, in particular rational homology spheres, and prove their diffeomorphism invariance. This paper is a revised version of math.DG/9701010. Some typos are removed.