No universal trading strategy exists due to mathematical impossibilities.
problem The impossibility of universally winning trading strategies in competitive markets.
method Three mathematical paradigms: measure-theoretic, No-Free-Lunch theorem, and adversarial Cantor diagonalization.
result No-arbitrage and free-lunch principles are mathematically precluded in competitive markets.
Market competition depends on computational complexity, P != NP makes it impossible.
problem Competitive market outcomes require computational intractability.
method Analyzes the computational hardness of collusion detection in markets.
result If P != NP, collusion detection is computationally infeasible, making collusion unstable.
Study shows how competition affects learning in matching markets, proving it's possible to balance stability, fairness, and regret.
problem How competition affects learning in matching markets and the impossibility of simultaneously guaranteeing stability and low optimal regret.
method Modeling a two-sided matching market with bandit learners and adding components of costs and transfers.
result It is possible to simultaneously guarantee stability, low optimal regret, fairness in the distribution of regret, and high social welfare.
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy to construct diffusion models which are both diverse and free of arbitrage. Can o…
The practice of valuation by marking-to-market with current trading prices is seriously flawed. Under leverage the problem is particularly dramatic: due to the concave form of market impact, selling always initially causes the expected leverage to increase. There is a critical leverage above which it is impossible to e…
No fair and strategy-proof automated market maker exists for more than two assets.
problem Designing a fair and strategy-proof automated market maker for multiple assets.
method Analyzing the weighted-product family of aggregation rules and their properties.
result No aggregation rule is both fair and strategy-proof for more than two assets.
The market efficiency hypothesis has been proposed to explain the behavior of time series of stock markets. The Black-Scholes model (B-S) for example, is based on the assumption that markets are efficient. As a consequence, it is impossible, at least in principle, to "predict" how a market behaves, whatever the circums…
The paper derives market-based correlations between asset prices and returns.
problem Market assumptions of constant trade volumes and past values are inaccurate.
method Derives expressions of correlations based on statistical moments and trade volumes.
result Market-based correlations are essential for traders, banks, and funds.
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is the strategy for…
The study confirms that market volatility can be explained by correlated metaorders impacting prices in a square-root fashion.
problem Explaining market volatility using metaorders and their impact.
method Generated synthetic market data and analyzed the correlation between order flow and returns.
result The square-root law of market impact is confirmed and can be measured from anonymized trade data.
Investment strategies in financial markets can lead to instability due to market impacts.
problem Market impacts make it impossible for investors to accurately optimize their strategies.
method Built an agent-based model with technical analysis strategy agents to investigate optimization instability.
result Investment strategies' parameters never converged but continued to change, leading to unstable market price evolution.
The paper models market dynamics using a limit order book system to explain slippage and inefficiency.
problem Inefficiency in matching markets due to structural liquidity constraints and slippage.
method Introduces a market microstructure framework with a latent preference state matrix and a dynamic discrete choice execution model.
result Persistent slippage and regional invariance of preference orderings are explained by liquidity thresholds.
Four-dimensional Einstein Dehn filling is impossible.
problem Complex-hyperbolic Einstein Dehn filling in four dimensions.
method Proof of impossibility.
result Complex-hyperbolic Einstein Dehn filling cannot be performed in dimension four.
We consider dynamics of financial markets as dynamics of expectations and discuss such a dynamics from the point of view of phenomenological thermodynamics. We describe a financial Carnot cycle and the financial analogue of a heat machine. We see, that while in physics a perpetuum mobile is absolutely impossible, in ec…
The efficient market hypothesis has been considered one of the most controversial arguments in finance, with the academia divided between who claims the impossibility of beating the market and who believes that it is possible to gain over the average profits. If the hypothesis holds, it means, as suggested by Burton Ma…
The bubble is a controversial and important issue. Many methods which based on the rational expectation have been proposed to detect the bubble. However, for some developing countries, epically China, the asset markets are so young that for many companies, there are no dividends and fundamental value, making it difficu…
Study finds similar companies in Dhaka Stock Exchange using technical data.
problem Analyzing all companies in Dhaka Stock Exchange is impractical.
method Used technical data to identify companies moving together.
result Technical data can reveal company relationships without fundamental data.
Machine fairness is impossible to achieve fully due to historical biases.
problem Machine learning models inherit biases from historical data, making it impossible to satisfy fairness metrics simultaneously.
method Presented a causal perspective to the impossibility theorem of fairness.
result It is impossible to satisfy fairness metrics like demographic parity, equal opportunity, and equalized odds simultaneously.
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough classes of distribution functions too. It is shown that there exists a nonzero po…
Improved forecasting of financial risk using Diffusion-Copula framework.
problem Capturing complex, asymmetric dependence structures in financial markets.
method Explicitly decouples marginal distribution learning from dependence structure using Mixture Density Networks and Classification-Diffusion Copula.
result Superior performance in forecasting systemic extremes of marginal and joint events.
In this article we prove the impossibility of some disentanglement puzzles, first building mathematical models that reflect the essential characteristics of these puzzles.
TWM doesn't reduce delta in PDLPs, proving impossibility.
problem TWM in PDLPs doesn't uniformly reduce portfolio delta.
method Proved TWM's condition is self-contradictory and showed impossibility.
result No TWM can uniformly reduce portfolio delta.
An impossibility result shows limitations in learning symmetries and equivariant functions.
problem Learning symmetries and equivariant functions simultaneously is impossible under certain conditions.
method Careful study of approximation for groups and semigroups, analysis of neural networks.
result Linearly equivariant networks can be used to learn equivariant functions, but group-convolutional networks have limitations.
The paper proves ADL mechanisms face a trilemma and optimizes them for fairness, revenue, and exchange solvency.
problem The impossibility of a perpetual futures exchange achieving solvency, revenue, and fairness.
method Formal model of ADL, proving trilemma, and analyzing three ADL mechanisms.
result Optimized ADL mechanisms can reduce trader losses while maintaining exchange solvency.
Large language models can't efficiently reason conditionally in a distribution-free setting.
problem Impossibility of conditional PAC-efficient reasoning in large language models.
method Proof of impossibility in a distribution-free setting for non-atomic input spaces.
result Any algorithm achieving conditional PAC efficiency must defer to the expert model with high probability.
Deep learning LSTM predicts stock prices for portfolio design in Indian sectors.
problem Predicting stock prices in Indian stock market.
method Long Short-Term Memory (LSTM) model for historical stock price prediction.
result Efficacy of LSTM model in predicting stock prices and informing investment decisions.
Every production-recycling iteration accumulates an inevitable proportion of its matter-energy in the environment, lest the production process itself would be a system in perpetual motion, violating the second law of Thermodynamics. Such high-entropy matter depletes finite stocks of ecosystem services provided by the e…
No feature ranking can be faithful, stable, and complete when features are collinear.
problem The impossibility of creating a feature ranking that is simultaneously faithful, stable, and complete when features are collinear.
method Proving the impossibility, quantifying it for four model classes, resolving it via ensemble averaging (DASH), and machine-verifying it with Lean 4 theorems.
result No method lies outside the dichotomy of faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods (stable, reporting ties for symmetric features).
Two impossibility theorems show formal alignment certification is impossible for AI systems.
problem Formal certification of AI alignment over open-ended domains is impossible.
method Two independent impossibility theorems: Semantic and Statistical barriers.
result No procedure can simultaneously satisfy soundness, completeness, and tractability.
Paper proves impossibility of three desirable properties in node embedding.
problem Understanding limitations of node embedding methods.
method Axiomatic approach to node embedding, proving impossibility of three properties.
result No node embedding method can satisfy all three desirable properties simultaneously.
Study uses agent-based simulation to analyze impact of OBI strategy on financial markets.
problem Improving execution in markets with supply-demand imbalance.
method Built an execution algorithm that accounts for OBI, tested it in artificial markets.
result OBI strategy can improve execution, especially in volatile markets.
A new method for variable importance measures without impossible data.
problem Using impossible data for variable importance measures in black box models.
method Cohort Shapley, a method grounded in economic game theory using only observed data.
result Cohort Shapley provides a more trustworthy explanation of black box models' decisions.
The prediction of a stock market direction may serve as an early recommendation system for short-term investors and as an early financial distress warning system for long-term shareholders. Many stock prediction studies focus on using macroeconomic indicators, such as CPI and GDP, to train the prediction model. However…
The study of tiling homology on flat surfaces, proving impossibility of certain tilings.
problem Proving the non-existence of polyomino tilings on specific square-tiled surfaces.
method Study of homology groups for topological tilings, using coloring proofs.
result Several results about the non-existence of polyomino tilings on certain square-tiled surfaces.
Researchers prove it's impossible to partially recover graph alignments in certain conditions.
problem Recovering vertex correspondence between two random graphs with correlated edges.
method Used the probabilistic method to build automorphisms between tree components of a subcritical Erdös-Rényi graph.
result Proved an impossibility result for partial recovery in the sparse regime with constant average degree and correlation.
Paper proposes a model to predict stock prices using historical and sentiment data.
problem Improving accuracy in predicting stock prices.
method Integrates historical and sentiment data to predict stock prices using LSTM.
result Improved accuracy in predicting stock prices.
Hass and Scott's example of a 4-valent graph on the 3-punctured sphere that cannot be realized by geodesics in any metric of negative curvature is generalized to impossible configurations filling surfaces of genus n with k punctures for any n and k.
We investigate default-free bond markets where the standard relationship between a possibly existing bank account process and the term structure of bond prices is broken, i.e. the bank account process is not a valid numéraire. We argue that this feature is not the exception but rather the rule in bond markets when star…
RL improves market making with historical data time travel.
problem Limited ability to simulate and fully appraise the impact of actions in competitive systems.
method Introduces 'consistent data time travel' to adjust historical data time index.
result Significant improvement in agent's gain with data time travel.
The purpose of this paper is to showcase trading strategies that give solutions to three difficult and intriguing problems in business finance, economics and statistics. The paper discusses trading strategies for both commodities and stocks but the main focus is on stock market trading at the New York Stock Exchange. P…
Model shows AI adoption amplifies financial market risk through prediction, herding, and cognitive dependency.
problem Systemic risk in financial markets due to AI adoption.
method Developed a unified model within an extended rational expectations framework, incorporating endogenous adoption, performative prediction, algorithmic herding, and cognitive dependency.
result Systemic risk multiplier grows superlinearly with AI penetration, implying tail-loss amplification of 18-54%.
This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target …
New protocol identifies impossible edge orientations in causal graphs.
problem Causal-discovery algorithms cannot distinguish edge directions without assumptions.
method Discrete impossibility certificates and oracle queries.
result Upper bound of 1+K expert interactions for DAG recovery. Proposes a resampling method to compare uplift models with uncertainty.
problem Uncertainty in estimating uplift curves when full population data is unavailable.
method Two-step sampling procedure and resampling-based approach.
result Validates the proposed method through simulations and real data applications.
Deep learning models predict stock prices with high accuracy and speed.
problem Precise prediction of stock prices in an efficient market.
method Design and training of ten deep learning regression models.
result Models achieve high accuracy in forecasting stock prices of an auto sector company.
Researchers prove inner product recovery is impossible in latent space models.
problem Recovering inner products in latent space models with random geometric graphs.
method Rate-distortion theory applied to Gaussian or spherical latent locations.
result Impossible to recover inner products if dimensionality exceeds nh(p), matching positive results' conditions. AdaBoost's success explained through noise influence measure.
problem Understanding why AdaBoost is a successful classifier.
method Introduced a measure of noise influence (ION) to explain AdaBoost's success.
result ION decreases with iteration number and base learner complexity.
Proving the existence of speculative financial bubbles even a posteriori has proven exceedingly difficult so anticipating a speculative bubble ex ante would at first seem an impossible task. Still as illustrated by the recent turmoil in financial markets initiated by the so called subprime crisis there is clearly an ur…