This paper introduces cluster exchange groupoids for Coxeter-Dynkin diagrams and finds their fundamental groups are braid groups.
problem Understanding the fundamental groups of cluster exchange groupoids for Coxeter-Dynkin diagrams.
method Introduced cluster exchange groupoids for Coxeter-Dynkin diagrams and showed the fundamental group isomorphic to braid groups.
result The fundamental group of the exchange groupoid for a Coxeter-Dynkin diagram is the braid group associated with the diagram.
Study exchange option pricing with stochastic volatility and correlation.
problem Pricing exchange options under stochastic volatility and correlation.
method Approximation using a closed-form solution with Taylor expansion.
result Numerical results show the effectiveness of the proposed method.
Unified framework for representation and causal structure learning using exchangeable data.
problem Identifying latent representations or causal structures in non-i.i.d. data.
method Identifiable Exchangeable Mechanisms (IEM) framework for representation and structure learning.
result New insights and identifiability results for causal structure and representation learning.
We prove that under fairly general conditions an iterated exchange move gives infinitely many non-conjugate braids. As a consequence, every knot has infinitely many conjugacy classes of n-braid representations if and only if it has one admitting an exchange move.
Simulation study evaluates causal ML models under confounding violations.
problem Assessing conditional exchangeability in causal machine learning models.
method Simulation study with varying confounding, sample size, and NCO structures.
result Causal ML models fail to recover true treatment effect heterogeneity under violations of conditional exchangeability.
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
Study approximates operators on labelled conditional distributions for non-exchangeable systems.
problem Approximating operators on constrained probability measures for non-exchangeable systems.
method Combines cylindrical approximations and DeepONet-type neural architecture for finite-dimensional representations.
result Establishes a universal approximation theorem for continuous operators on Mλ. New method identifies causal structure in exchangeable data.
problem Existing causal discovery methods struggle with i.i.d. data.
method Exchangeable data provides richer conditional independence structure.
result Exchangeable data allows for unique causal structure identification.
The exchange algorithm is studied for its convergence and asymptotic variance.
problem Theoretical limitations of the exchange algorithm in sampling from doubly-intractable distributions.
method Theoretical analysis of the exchange algorithm's convergence speed and asymptotic variance.
result The exchange algorithm converges at a geometric rate and satisfies a Central Limit Theorem.
It is assumed that under suitable economic and information-theoretic conditions, market exchange rates are free from arbitrage. Commodity markets in which trades occur over a complete graph are shown to be trivial. We therefore examine the vector space of no-arbitrage exchange rate ensembles over an arbitrary connected…
In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant…
C-SymmPI provides near-conditional coverage for structured data with group symmetries.
problem Establishing near-conditional coverage guarantees for structured data with group symmetries.
method Developed a framework C-SymmPI that achieves near-conditional coverage under general data structures with group symmetries.
result Near-conditional coverage guarantees for structured data with group symmetries.
We analyze high-resolution foreign exchange data consisting of 20 million data points of USD-JPY for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations. A conditional probability density analysis clearly shows the existence of trend-following movements at time scale…
New framework models non-exchangeable networks with latent orders and graphons.
problem Modeling non-exchangeable network data with complex dependencies.
method Latent orders and graphon-based approach for adjacency matrix probabilities.
result Consistent estimation and clustering of latent network structure.
We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is modelled on the graph of triangulations of the marked surface, we show that the univ…
Study compares costs and arbitrage in CEXs vs DEXs, finding DEXs better for large trades.
problem Comparing transaction costs and arbitrage in crypto exchanges.
method Comprehensive dataset analysis of transaction costs and no-arbitrage deviations.
result Fixed gas fees in DEXs impose a significant burden on small trades, while CEXs offer more competitive costs for larger trades.
Framework handles both exchangeable and non-exchangeable event sequences without tuning.
problem Handling both exchangeable and non-exchangeable event sequences efficiently.
method Parametric Hawkes-process-inspired conditional probability mass function with variational inference.
result Competitive computational and predictive performance against state-of-the-art methods.
This paper examines the intra-day seasonality of transacted limit and market orders in the DEM/USD foreign exchange market. Empirical analysis of completed transactions data based on the Dealing 2000-2 electronic inter-dealer broking system indicates significant evidence of intraday seasonality in returns and return vo…
QLAMMP optimizes fees on AMMs using Q-Learning.
problem Static AMMs cannot adapt to market changes, leading to high slippage.
method Developed a Q-Learning Agent (QLAMMP) to learn optimal fee rates.
result QLAMMP consistently outperforms static AMMs under various market conditions.
Concentration of infinitely exchangeable sequences with bounded-difference constants
problem Quantifying uncertainty in AI benchmarks
method Using a mixture-free Hoeffding-type bound
result Tight, mixture-free Hoeffding-type bound for zero-sum linear contrasts
The currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the …
Although technical trading rules have been widely used by practitioners in financial markets, their profitability still remains controversial. We here investigate the profitability of moving average (MA) and trading range break (TRB) rules by using the Shanghai Stock Exchange Composite Index (SHCI) from May 21, 1992 th…
Optimizes trading in CFMMs and exchanges using deep learning.
problem Optimizing trading strategies in CFMMs and exchanges.
method Develops a model accounting for interaction between CFMMs and exchanges, employs deep Galerkin method to solve dynamic programming equation.
result Optimal strategy outperforms naïve strategies and is not prone to price slippage.
New method for robust prediction valid under non-exchangeable data.
problem Non-exchangeability in data violates robustness of common CP methods.
method Introduces efficient CP approach for general non-exchangeable data.
result Produces provably valid confidence sets for non-exchangeable data.
Decentralized detection avoids sharing data, controls false discoveries.
problem Global false discovery rate control in decentralized novelty detection.
method Quantized surrogate models for low-precision sharing, preserving exchangeability.
result Quantized composite scores maintain competitive statistical power with reduced communication.
New method constructs synthetic treatment groups without mean exchangeability assumption.
problem Violations of mean exchangeability assumption in randomized controlled trials.
method Weighted mixture of treatment groups from source populations, minimizing conditional maximum mean discrepancy.
result Asymptotic normality of synthetic treatment group estimator established.
We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over observations is invariant under permutation: this property lies at the heart of Ba…
Validates conformal prediction for network data under non-uniform sampling.
problem Validity of conformal prediction for network data under non-representative sampling.
method Interprets sampling mechanisms as selection rules, studies validity conditional on selection events, uses permutation invariance and joint exchangeability.
result Finite-sample validity of conformal prediction for certain selection events and asymptotic validity for random walk sampling.
The paper investigates cyclic arbitrage opportunities in decentralized exchanges.
problem Price discrepancies in decentralized exchanges lead to arbitrage opportunities.
method Theoretical framework and analysis of transaction-level data.
result Traders have executed over 292,606 cyclic arbitrages over eleven months, exploiting more than 138 million USD in revenue.
Framework to generalize impermanent loss for decentralized exchanges.
problem Difficult analysis of impermanent loss due to diverse market maker algorithms and fee structures.
method Developed a framework to generalize impermanent loss for constant function market makers with optional concentrated liquidity.
result Identified conditions for profitability of liquidity provisioning.
In the analysis of machine learning models, it is often convenient to assume that the parameters are IID. This assumption is not satisfied when the parameters are updated through training processes such as SGD. A relaxation of the IID condition is a probabilistic symmetry known as exchangeability. We show the sense in …
Temporal mixture ensemble predicts cryptocurrency exchange volumes better than traditional methods.
problem Intraday volume forecasting in cryptocurrency markets.
method Temporal mixture ensemble model using transaction and order book data.
result The model outperforms traditional time series and machine learning methods.
Detect anomalies in complex networks using topological subspace detectors.
problem Detect anomalies in complex networks defined by simplicial complexes.
method Formulate a hypothesis testing framework using Neyman-Pearson matched topological subspace detectors.
result Effective detection of anomalies in foreign currency exchange networks and other real-world data.
Any discussion on exchange rate movements and forecasting should include explanatory variables from both the current account and the capital account of the balance of payments. In this paper, we include such factors to forecast the value of the Indian rupee vis a vis the US Dollar. Further, factors reflecting political…
Numerical method for pricing exchange options with stochastic volatility and jumps.
problem Pricing exchange options under stochastic volatility and jump-diffusion dynamics.
method Method of lines (MOL) approach to simplify and solve the PDEs.
result Characterization of near-maturity American exchange option boundary and impact of model parameters.
This thesis explores supervised classification methods using Bayesian and exchangeability theories.
problem Assigning objects into predefined classes using training data and auxiliary information.
method Bayesian inductive theories and exchangeabilities (de Finetti and partition exchangeability).
result Optimal classifiers for different scenarios of object features and categories.
Novel method for time-series prediction with tighter confidence intervals.
problem Improving prediction intervals for time-series data.
method Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI) using adaptive weights.
result KOWCPI achieves narrower confidence intervals with guaranteed coverage.
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide new formulas for the di…
Currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the mark…
In this article, we investigate whether exchange rate risk is priced. We use a multivariate GARCH-in-Mean specification and test alternative conditional international CAPM versions. Our results support strongly the international asset-pricing model that includes exchange rate risk for both developed and emerging stock …
Simple models outperformed sophisticated ones in forecasting Turkish lira exchange rates.
problem Forecasting Turkish lira exchange rates through univariate techniques.
method Used several models including simple exponential smoothing to predict daily exchange rates.
result Simple exponential smoothing model outperformed all other alternatives.
The paper addresses errors in online selective conformal prediction and proposes new strategies to ensure valid inference.
problem Online selective conformal prediction's exchangeability issues and false coverage rate control problems.
method Evaluation and correction of existing calibration selection strategies, proposing new ones that preserve exchangeability.
result Novel calibration selection strategies ensure both selection-conditional coverage and FCR control.
Optimizes routing in decentralized exchanges with gas fees.
problem Routing in decentralized exchanges with fixed gas fees.
method General optimization framework with mixed-integer model, incorporating gas fees.
result Explicit Karush-Kuhn-Tucker system linking prices, fees, and activation.
Synthetic data can be used to ask more questions and accelerate discovery with provable validity guarantees.
problem Valid inference with synthetic data
method Task exchangeability
result Provable validity guarantees for synthetic data inference
We characterize the class of exchangeable feature allocations assigning probability Vn,k∏l=1kWmlUn−ml to a feature allocation of n individuals, displaying k features with counts (m1,…,mk) for these features. Each element of this class is parametrized by a countable matrix V…
New approaches improve uncertainty quantification in autoregressive models for sequence data.
problem Uncertainty quantification in autoregressive models for exchangeable sequences.
method Study of inferential and architectural biases for autoregressive models, focusing on multi-step inference.
result Custom architectures are necessary for multi-step inference to ensure exchangeability.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the…