We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes. Moreover, we show th…
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48 results for “partial exchangeability”
Derives Black-Scholes model without stochastic calculus or PDEs.
problem Deriving the Black-Scholes model without advanced math.
method Continuum limit of Binomial tree approach.
result Derives Black-Scholes model and exchange-option generalization.
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamicsq-fin.MF
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
Lead-lag relationships among assets represent a useful tool for analyzing high frequency financial data. However, research on these relationships predominantly focuses on correlation analyses for the dynamics of stock prices, spots and futures on market indexes, whereas foreign exchange data have been less explored. To…
Data-aware activation function customization reduces neural network error.
problem Current neural networks lack consideration for specific activation functions.
method Linear algebraic explanation and Diaconis-Shahshahani Approximation Theorem criteria for activation functions.
result Using an even activation function like seagull can reduce neural network error by orders of magnitude.
We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 stocks listed on the Shanghai and Shenzhen stock exchanges. Both raw correlation matrix and partial correlation matrix with respect to the ma…
The value of an asset in a financial market is given in terms of another asset known as numeraire. The dynamics of the value is non-stationary and hence, to quantify the relationships between different assets, one requires convenient measures such as the means and covariances of the respective log returns. Here, we dev…
It is known since 40 years old paper by M. Keane that minimality is a generic (i.e. holding with probability one) property of an irreducible interval exchange transformation. If one puts some integral linear restrictions on the parameters of the interval exchange transformation, then minimality may become an "exotic" p…
Proposes a new method for completing swap cycles in decentralized exchanges.
problem Completing swap cycles in decentralized exchanges efficiently and without slippage.
method Introduces an asset matrix formulation to verify and complete CoW cycles using graph traversal and imbalance correction.
result Demonstrates efficient discovery and insertion of synthetic orders for atomic cycle closure.
Study Nash equilibrium between broker and informed trader in dealer and lit markets.
problem Nash equilibrium between broker and informed trader in dealer and lit markets with partial information.
method Convex analysis, FBSDEs, polynomial approximation.
result Existence and uniqueness of Nash equilibrium for short time horizons.
Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities relate…
Exchange uses incentives to optimize limit order book dynamics.
problem Optimizing market liquidity in fragmented electronic markets.
method Modeling limit order book as SPDE and using control theory to design incentives.
result Exchange can design incentives to modify order book shape and increase liquidity.
High Frequency Market Makingq-fin.TR
Since they were authorized by the U.S. Security and Exchange Commission in 1998, electronic exchanges have boomed, and by 2010 high frequency trading accounted for over 70% of equity trades in the US. Such markets are thought to increase liquidity because of the presence of market makers, who are willing to trade as co…
We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool. We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by Lévy processes. Effect…
Paper establishes MLE consistency for market microstructure models.
problem Estimating parameters in partially observed diffusion models.
method Tractable sufficient condition for MLE consistency based on stationary distribution.
result Maximum likelihood estimators are consistent for market microstructure parameters.
A game-theoretic analysis of DEX competition through dynamic trading fees.
problem Competition between decentralized exchanges (DEXs) and their impact on trading fees and slippage.
method Characterization of an approximate Nash equilibrium via coupled system of partial differential equations and closed-form expressions for equilibrium fees.
result The equilibrium trading fees shift from the oracle price to a weighted average of the oracle and competitors' exchange rates under competition.
We investigate a classification problem using multiple mobile agents capable of collecting (partial) pose-dependent observations of an unknown environment. The objective is to classify an image over a finite time horizon. We propose a network architecture on how agents should form a local belief, take local actions, an…
Revisits Jarrow & Turnbull model for credit and liquidity risk.
problem Modeling credit and liquidity risk in financial markets.
method Uses foreign exchange analogy and partially observable exchange rate.
result Derives tractable term structure models and explicit valuation formulae.
We propose a method for detection and prediction of native and synthetic iceberg orders on Chicago Mercantile Exchange. Native (managed by the exchange) icebergs are detected using discrepancies between the resting volume of an order and the actual trade size as indicated by trade summary messages, as well as by tracki…
Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into K clusters with exchangeable dependence; t…
It is well-known that the distribution over functions induced through a zero-mean iid prior distribution over the parameters of a multi-layer perceptron (MLP) converges to a Gaussian process (GP), under mild conditions. We extend this result firstly to independent priors with general zero or non-zero means, and secondl…
The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap under which a predetermined fixed leg and the floating leg of the rea…
Inverse Statistics in the Foreign Exchange Marketcond-mat.other
We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) in the price of an investment. The analysis is performed for the Deutsch mark (DM…
Unified approach for predicting missing segments in partially observed functions.
problem Predicting missing segments in partially observed functions with complex dependence and irregular noise.
method Unified registration and prediction approach under the conformal prediction framework, integrating amplitude and phase components.
result Effective prediction bands with finite-sample marginal coverage guarantees under weak assumptions.
From Partial Exchangeability to Predictive Probability: A Bayesian Perspective on Classificationstat.ME
Bayesian model improves classification performance with flexible uncertainty modeling.
problem Improving classification performance with flexible uncertainty modeling.
method Combines Gaussian process and Dirichlet process priors for latent function and link function, respectively.
result Outperforms standard logistic regression on simulated data.
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.
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an Itô's diffusion with time--dependent drift, and with a full matrix of corre…
Study on pricing American Exchange options using Lévy processes.
problem Pricing American Exchange options driven by Lévy processes.
method Represented American Exchange options as European options plus early exercise premium; studied properties of free boundary and provided an approximative formula.
result Developed an approximative formula for American Exchange options.
Four geometries govern sequential and distribution-free inference.
problem Sequential and distribution-free inference challenges.
method Four distinct admissibility geometries.
result Four classes of admissible procedures are pairwise non-nested.
Optimal crypto order execution using cross-exchange signals.
problem Maximizing order execution efficiency in cryptocurrency markets.
method Reinforcement learning applied to cross-exchange data.
result Cross-exchange signals improve optimal execution outcomes.
New method for selective prediction under interventions learns causal structure from data.
problem Tight uncertainty sets in selective conformal prediction under unknown interventional settings.
method Partial causal structure learning for descendant indicators, contamination-robust coverage theorem, algorithms for descendant discovery and distance estimation.
result Valid selective conformal prediction under contamination up to 30% with controlled coverage.
This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP …
Networked Control of Nonlinear Systems under Partial Observation Using Continuous Deep Q-Learningcs.LG
In this paper, we propose a design of a model-free networked controller for a nonlinear plant whose mathematical model is unknown. In a networked control system, the controller and plant are located away from each other and exchange data over a network, which causes network delays that may fluctuate randomly due to net…
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare v…
Regional Inequality Simulations Based on Asset Exchange Models with Exchange Range and Local Support Biasphysics.soc-ph
New models reduce regional inequality by adjusting exchange range and asset distribution bias.
problem Reduction of regional inequality in economic systems.
method Proposed new asset exchange models with spatial exchange range and local support bias to adjust asset distribution and circulation rates.
result Achieved asset distribution from over-concentration to exponential and eventually normal, reducing Gini coefficient.
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …
Investigate using LETFs to outperform benchmarks, finding them more likely to succeed.
problem The controversy and popularity of LETFs in constructing portfolios.
method Systematic investigation using IR-optimal strategies with LETFs and VETFs, including neural network-based approaches.
result IR-optimal strategies with LETFs outperform benchmarks and achieve partial stochastic dominance.
Wealth Distributions in Asset Exchange Modelsphysics.soc-ph
How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange rules --- transactions that…
The team predicts foreign exchange rates using clustering and attention models.
problem Complexity and unexpected events in foreign exchange markets.
method Clustering and attention models applied to historical data.
result Improved event-driven price prediction for oversold scenarios.
P3LS preserves privacy while integrating data across companies.
problem Privacy concerns in cross-organizational data exchange and integration.
method Privacy-preserving federated learning technique using SVD-based PLS and random masks.
result Improves prediction performance on process-related indicators.
Wealth Distributions in Models of Capital Exchangecond-mat.stat-mech
A dynamical model of capital exchange is introduced in which a specified amount of capital is exchanged between two individuals when they meet. The resulting time dependent wealth distributions are determined for a variety of exchange rules. For ``greedy'' exchange, an interaction between a rich and a poor individual r…
Study finds recurring patterns in cryptocurrency volatility and liquidity.
problem Recurring patterns in volatility and liquidity of major cryptocurrencies.
method Data from two centralized exchanges and a decentralized exchange analyzed for patterns.
result Systematic patterns in volatility and liquidity across different timeframes.
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.
Kalman Filter in the Problem of the Exchange and the Inflation Rates Adequacy To Determining Factorsq-fin.MF
Study finds relevance of exchange and inflation rates to economic factors.
problem Determining the relevance of exchange and inflation rates to economic factors.
method Introduced concept of adequacy, established positive relation between exchange and inflation rates and other economic factors.
result Close positive relation found between exchange and inflation rates and other economic factors.
The article improves the display of acceptable exchange ratios for merging companies.
problem Determining feasible exchange ratios for merging companies.
method Exploits a diagrammatic approach to display the bargaining region.
result Shares face upper and lower bounds for acceptable exchange ratios.
Framework for systemic risk modeling using jointly exchangeable arrays.
problem Systemic risk in insurance portfolios with interactions.
method Jointly exchangeable arrays, central limit theorems, simulation-based validation.
result Asymptotic approximations for total portfolio losses in large portfolios over long time horizons.
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.