Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.
problem Characterizing left-orderability in HNN extensions of groups.
method Analyzes HNN extensions of torsion-free nilpotent groups and left-orderable groups.
result Constructs examples of non-left-orderable HNN extensions of left-orderable groups.
The study examines how limit-order book resilience changes after effective market orders in Chinese stocks.
problem Understanding the resilience of limit-order books after liquidity shocks.
method Empirical analysis of order flow data from Chinese stocks, focusing on bid-ask spread, LOB depth, and order intensity.
result Traders are more likely to submit effective market orders when the bid-ask spread is low, same-side depth is high, and opposite-side depth is low.
New criterion links circular-orderability to left-orderability.
problem Understanding when circularly-orderable groups are left-orderable.
method Introducing a criterion based on the product of a group with integers.
result Groups are left-orderable if their product with integers is circularly-orderable.
The paper analyzes order positions and queues in limit order books.
problem Understanding the dynamics of order positions and queues in limit order books.
method Fluid and diffusion limits, fluctuations analysis, explicit expressions derivation.
result Explicit analytical expressions for various quantities in limit order books.
The study examines order flow patterns in NASDAQ stocks, finding that limit order placement inside the spread is influenced by spread dynamics.
problem Understanding the dynamics of order flow in NASDAQ stocks.
method Analysis of order flow data for different NASDAQ stocks, focusing on limit orders, market orders, and their placement.
result Limit order placement inside the spread is strongly influenced by spread dynamics, while most orders are placed outside the spread.
The paper characterizes L-space 3-manifolds using quandle orderability.
problem Characterizing L-space 3-manifolds using quandle orderability.
method Using quandles and their extensions, the paper investigates orderability and circular orderability conditions.
result The n-quandle Qn(L) of a link quandle is not right circularly orderable. Optimal stock trading strategy with market orders and limit orders in a risky market.
problem Finding the best time and amount to place market and limit orders to minimize costs.
method Analyzes single and multi-period models with limit and market orders, considering liquidity risk.
result Optimal placement of market and limit orders can be determined under different market conditions.
The paper discusses conditions for equality of two distributions under partial orders.
problem Establishing conditions for stochastic equality of two distributions under partial orders.
method Analyzes convex and supermodular orderings to find conditions for equality.
result Conditions for stochastic equality of two distributions under convex and supermodular orderings are established.
Algorithm confirms non-order-preserving braids, proving infinite family not order-preserving.
problem Determining if a braid is non-order-preserving.
method Algorithm that checks non-order-preserving property of braids.
result Infinite family of simple 3-braids are not order-preserving.
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.
The paper explores orderability in link quandles and provides various results.
problem Orderability of link quandles and its interconnections with link groups.
method Develops a general theory of orderability, proves specific cases, and explores interconnections.
result Link quandles of most non-trivial torus links are not right-orderable.
We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic result…
Map quandle orders to actions, characterize isolated orders, and prove no isolated right orders.
problem Characterizing isolated orders on quandles and proving the absence of certain orders.
method Construct a continuous map from orders to actions, use strong rigidity, and analyze specific cases.
result No isolated right orders on free quandles, except for specific cases.
The paper defines circular orderability for quandles and explores their properties.
problem Understanding the structure of quandles through circular orderings.
method Introduced circular orderability for quandles, showed embedding properties, and provided examples.
result Spaces of circular orderings embed in the space of all orderings, and examples of non-circularly orderable quandles are given.
Paper finds conditions for free product of circularly-ordered groups to have a circular ordering.
problem Conditions for free product of circularly-ordered groups to admit a circular ordering.
method Established a categorical framework to amalgamate left-ordered central extensions, applying work of Bludov and Glass.
result Necessary and sufficient conditions for the free product with amalgamation of circularly-ordered groups to admit a circular ordering.
Multivariate Hawkes processes analyze order dynamics in financial markets.
problem Complex interactions between order timing and size in financial markets.
method Multivariate Hawkes processes with nonparametric estimation.
result Simple volume-time independence models are inadequate for financial data.
Bi-orderable groups from left-orderable ones, showing non-profinite properties.
problem Non-profinite properties in bi-orderability and generalized torsion elements.
method Using fiber products to construct bi-orderable groups, showing non-profinite properties.
result Bi-orderability and generalized torsion elements are not profinite properties.
Study finds power-law tails in order imbalance distributions of Chinese stocks.
problem Analyzing the distribution of order imbalance in Chinese stock markets.
method Examined order imbalance based on order number and size, analyzed distributions at different time scales.
result Order imbalance distributions exhibit power-law tails with varying tail indices across stocks.
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persistence of the order flow with market efficiency is a subtle issue. A poss…
Paper introduces techniques to learn higher-order programs, improving predictive accuracy and reducing learning times.
problem Expressing and learning complex programs in ILP.
method Extending meta-interpretive learning to support higher-order definitions as background knowledge.
result Learning higher-order programs reduces hypothesis space and sample complexity, improving predictive accuracy and reducing learning times.
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…
New conditions for circular orderability of direct products, linking to left-orderability of groups.
problem Conditions for circular orderability of direct products GimesZ/nZ. method Cohomological conditions and characterizations for left-orderability.
result New characterization for left-orderability of fundamental groups of rational homology 3-spheres.
New features capture the order of data streams.
problem Handling ordered moments in massive data streams.
method Introducing features for ordered moments.
result Theoretical guarantees for learning algorithms.
Proposes a model for simulating limit order books with state-dependent intensities.
problem Simulating the dynamics of limit order books with varying intensities of order submission.
method Developed a parametric model with state-dependent intensities for limit orders, market orders, and cancellations. Introduced new models for order placement and cancellation selection.
result The proposed model accurately simulates the dynamics of limit order books and outperforms standard Poisson models.
We study the dynamics of order flows around large intraday price changes using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a significant reversal of price for both intraday price decreases and increases with a permanent price impact. The volatility, the volume of different types of orders, the b…
Extends spectral order definition to contact manifolds with convex boundary.
problem Defining spectral order for contact manifolds with convex boundary.
method Extends Heegaard Floer homology definition and proves bounds on contact structures.
result Establishes bounds on contact structures and spectral order.
New criterion for bi-ordering free groups under automorphisms.
problem Bi-ordering free groups under automorphisms.
method New criterion for bi-ordering free groups.
result Fundamental group of the magic manifold is bi-orderable.
The paper finds the smallest order closed sublattice containing a given sublattice in vector lattices.
problem Identifying the smallest order closed sublattice containing a given sublattice in vector lattices.
method Analyzing the order closure and second order closure of sublattices.
result The smallest order closed sublattice containing a sublattice Y is often the second order closure of Y. A framework models order book dynamics using point processes and mass transport.
problem Capturing the complex dynamics of limit order books.
method Combines spatial point process for order flow and mass transport operator for market clearing.
result Provides insights into the interplay between order flow and price dynamics.
Finite concordance order 3-braid knots are ribbon.
problem Understanding finite concordance order 3-braid knots.
method Analyzing 3-braid knots of finite concordance order.
result Chiral 3-braid knots of finite concordance order are ribbon.
Paper derives second order approximations for limit order books.
problem Modeling fluctuations in price and volume processes.
method Second order approximation of infinite dimensional limit order book dynamics.
result Confidence intervals for optimal portfolio liquidation models.
Infinite order loose corks created.
problem Creating loose corks of infinite order.
method Constructing an infinite order loose cork.
result Demonstrated construction of an infinite order loose cork.
The paper explores circular orderability in 3-manifold groups, related to the L-space conjecture.
problem Circular orderability of 3-manifold groups and its relation to the L-space conjecture.
method Investigation of finite cyclic covers and Dehn surgeries to establish circular orderability.
result Circularly orderable fundamental groups of compact, connected, P^2-irreducible 3-manifolds are characterized.
New dynamics derived from Lie groups using 2nd order tangent groups.
problem Deriving dynamics on complex Lie groups.
method Using double cross product groups and 2nd order Euler-Lagrange equations.
result 2nd order Lagrangian dynamics on double cross product groups derived.
Improved stock price prediction model using generalized order flow imbalance.
problem Improving stock price prediction models using new order flow imbalance indicators.
method Proposed a generalized order flow imbalance construction method and applied it to CSI 500 stocks.
result Generalized Stationarized Order Flow Imbalance (log-GOFI) shows significant improvement in explaining stock price changes.
Optimizes high-frequency trading strategies in limit order books.
problem Impact of recent orders on future order submission rates.
method Discrete Markov chain model for LOB dynamics, Markov decision process for optimal order placement.
result Optimal policy using limit, cancellations, and market orders to maximize execution price.
Two price regimes identified in limit order books: close and far from quotes.
problem Understanding the distribution and behavior of limit orders in limit order books.
method Analysis of limit order book data in dimensions of price, time, lifetime, and volume.
result Identification of two distinct regimes in the limit order book: close and far from quotes.
MIC improves VAR order selection accuracy.
problem Order selection in VAR models for accurate forecasting.
method MIC based on expected squared error loss.
result MIC consistently estimates true VAR order.
In this paper we define nth order Hessian structures on manifolds and study them. In particular, when n=3, we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it certain class of connections} on the second-order tangent bundle of a manifold. Furt…
We develop a second-order model for limit order books in a single scaling regime.
problem Modeling price and volume dynamics in a limit order book with market and limit orders at a common time scale.
method Established a first- and second-order approximation for an infinite dimensional limit order book model.
result Proved the existence and uniqueness of a solution for the second-order approximation.
Large traders disrupt the market's long-term memory of order signs.
problem Long-term memory of market order signs is weakened by large traders.
method Analyzed over 6.7 billion trades to investigate the impact of large investment funds on market order dynamics.
result The long-term memory of market order signs is weaker when large investment funds trade in a directional manner and when their participation is high.
Study proposes a new GAN for realistic discrete financial orders.
problem Previous GANs generated fake orders in continuous spaces, not discrete.
method Introduced policy gradient for learning in discrete spaces.
result Model outperforms previous models in generated order distribution.
Proposes a stochastic model for limit order book dynamics.
problem Captures the dynamics of limit order books in financial markets.
method Develops a stochastic partial differential equation (SPDE) model with multiplicative noise.
result Shows efficient estimation and computation methods for the model.
To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the structure of transaction fees a…
New high-order compact scheme improves basket option pricing accuracy.
problem Improving accuracy in pricing European Put options on a basket of assets.
method Developed a second-order accurate in time and fourth-order accurate in space high-order compact scheme.
result Standard second-order schemes are significantly outperformed by the new scheme.
Order submission and cancellation are two constituent actions of stock trading behaviors in order-driven markets. Order submission dynamics has been extensively studied for different markets, while order cancellation dynamics is less understood. There are two positions associated with a cancellation, that is, the price…
New invariants show stronger virtual knot sets.
problem Classifying virtual knots using invariants.
method Defining F-order invariants using forbidden moves. result Set of F-order invariants is strictly stronger. A new GCN model learns higher-order neighbors without explicit adjacency matrix computation.
problem GCN's performance drops for deeper structures due to limited neighborhood information.
method Assumes higher-order neighbors are similar to first-order neighbors, learns weights through Lasso to minimize feature loss.
result HWGCN achieves state-of-the-art results on various datasets.