Optimal strategy found for minimizing loss in shopper's dilemma.
problem Minimizing loss in a two-period decision-making process.
method Derived from the two-envelope paradox and Black Friday promotion.
result Optimal strategy found to minimize expected loss.
The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.
This paper explores geometric insights into discrete R-congruences and their envelopes.
problem Understanding the ambiguity in discrete R-congruences and their envelopes.
method Analyzes discrete R-congruences that are enveloped by specific types of surfaces and maps.
result Discovers a 2-parameter family of discrete enveloping surfaces for discrete R-congruences.
This paper solves Siegel's paradox about future exchange rates.
problem Understanding future exchange rates and resolving Siegel's paradox.
method An unorthodox approach leading to an arbitrage-free solution.
result A formula describing all no-arbitrage forward exchange rates.
New pricing theory solves St. Petersburg paradox.
problem St. Petersburg Paradox unresolved for 280 years.
method Proposes new pricing theory with fair pricing rules.
result New pricing theory resolves the paradox.
Paper revisits five IF paradoxes using differential geometry.
problem Five paradoxes of Instantaneous Frequency in three-phase systems.
method Geometric interpretation of frequency to explain IF paradoxes.
result Revisits and explains five IF paradoxes through a common framework.
Karl Menger's 1934 paper on the St. Petersburg paradox contains mathematical errors that invalidate his conclusion that unbounded utility functions, specifically Bernoulli's logarithmic utility, fail to resolve modified versions of the St. Petersburg paradox.
This paper develops a cohomological hierarchy for bistable visual paradoxes.
problem Understanding the hierarchy of visual paradoxes built from bistable elements.
method Develops a cohomological hierarchy using Z2 coefficients and a discrete Stokes theorem. result Reveals a hierarchy of paradox classes from H0 through H2, refined at each degree by the relative/absolute distinction. A coin-flipping game paradox illustrates how conditional probability estimation can distort risk assessment.
problem Distortion of risk assessment due to incorrect conditional probability estimation.
method A coin-flipping game to illustrate the paradox of conditional probability estimation.
result Incorrect conditional probability estimation can lead to excessive risk bearing.
Simpson's paradox can invalidate the results of medical trials if an unobserved variable is considered.
problem The validity of medical trial results can be invalidated by an unobserved confounding variable.
method Simulated controlled trials to demonstrate the paradox.
result The results of a trial can be reversed by including an unobserved confounding variable.
New approach solves St. Petersburg paradox using randomness.
problem St. Petersburg paradox in game theory.
method Using Von Mises' axiom of randomness to determine cognitive strategies.
result Cognitive strategies can generate results not random, resolving paradox.
The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathemat…
Thompson Sampling shows polynomial regret for combinatorial semi-bandits with subgaussian rewards.
problem Finding optimal solutions in combinatorial semi-bandits with suboptimal sampling.
method Proposes Thompson Sampling with polynomial regret for linear combinatorial semi-bandits.
result Demonstrates 'mismatched sampling paradox' where knowing distributions can lead to worse performance.
A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is …
The paper tackles individualized decision-making under unmeasured confounding, providing a novel minimax solution and a paradox.
problem Unmeasured confounding in causal inference leads to biased estimates and affects individualized decision-making.
method The authors establish a formal link between individualized decision-making under partial identification and classical decision theory, providing a minimax solution and a paradox.
result A novel minimax solution for individualized decision-making/policy assignment is provided, and an interesting paradox is drawn.
A mathematical paradox shows secant planes don't always form a tangent plane, but some analogies hold with a specific vector product.
problem Secant planes of a two-variable smooth function do not always form a tangent plane, even for simple polynomials.
method Analogies with the one-variable case are explored, using Clifford's geometric vector product.
result Some analogies with the one-variable case still hold in the multi-variable context with a specific vector product.
Quantum framework explains human choices in ambiguity and risk.
problem Testing human choices in ambiguity and risk.
method Quantum-theoretic framework for decision-making under uncertainty.
result Quantum framework faithfully models human choices in ambiguity and risk.
We consider strategies of investments into options and diffusion market model. It is shown that there exists a correct proportion between "put" and "call" in the portfolio such that the average gain is almost always positive for a generic Black and Scholes model. This gain is zero if and only if the market price of ris…
New methods resolve conflicting treatment effect estimates in health tech assessments.
problem Conflicting conclusions from different sponsors analyzing the same data.
method Arbitrated indirect treatment comparisons (ArMAIC) targeting a common target population.
result Estimates treatment effects in a common target population, resolving the MAIC paradox.
Partial covariance factorizes in path diagrams, simplifying analysis.
problem Understanding partial covariance in complex diagrams.
method Factorization of partial covariance over nodes and edges.
result Simpson's paradox cannot occur in singly-connected diagrams.
Buying or selling assets leads to transaction costs for the investor. On one hand, it is well know to all market practionaires that the transaction costs are positive on average and present therefore systematic loss. On the other hand, for every trade, there is a buy side and a sell side, the total amount of asset and …
Researchers solved a geometry paradox for creased tubes.
problem Resolving the paradox of Gaussian curvature in creased tubes.
method Calculated Gaussian curvature in terms of rate of change of solid angle, dependent on fold angle and curvature.
result Gaussian curvature is zero overall despite the surface being doubly-curved.
Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions are considered. The solution of the paradox lies in the non-constant nature of re…
GenAI adoption paradoxically lowers ROE for U.S. banks, with spillovers but systemic risk concerns.
problem Productivity paradox and implementation costs in U.S. banking sector with AI adoption.
method Dynamic Spatial Durbin Models (DSDM) and Synthetic Difference-in-Differences (SDID) for causal inference.
result AI adoption leads to a 428-basis-point decline in ROE for banks, with spillovers but systemic risk implications.
This paper highlights the role of risk neutral investors in generating endogenous bubbles in derivatives markets. We find that a market for derivatives, which has all the features of a perfect market except completeness and has some risk neutral investors, can exhibit extreme price movements which represent a violation…
Introduces preference-robust decision making for risk models.
problem Ambiguity in risk functionals.
method Constructs ambiguity sets on distortion functions using Wasserstein distance and Bregman divergences.
result Derives closed-form expressions for worst- and best-case distortion risk measures.
Underrepresented scientists produce more novel work but it's undervalued.
problem Underrepresented groups in science face undervaluation of their innovations.
method Text analysis and machine learning of career data of over 1 million US doctoral recipients.
result Underrepresented groups produce more scientific novelty but their contributions are undervalued.
We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers v…
Osborne's paradox explained via Bayesian inference and superstatistics.
problem Osborne's paradox regarding stock price changes.
method Bayesian inference and superstatistics.
result Stock market returns are locally described by equilibrium statistical mechanics, globally by superstatistics.
Simplified NFT games discussed with methods for extracting value.
problem Issues influencing NFT games' structure and stability.
method Three methods for extracting value from NFT games.
result Various design constraints and mutual beneficial games.
New method uses correlation-ratio for transfer learning, improving target model inference.
problem Difficulty in meeting similarity condition for transfer learning.
method Introduces linear correlation-ratio for building accurate relationships between models.
result Improves inference on target model by transferring information from source models.
A model shows faster energy transition rewards flexible production more quickly.
problem Energy transition discourages investments in flexible production.
method Modeling future electricity prices from residual load, investigating revenues for various flexibility levels.
result Faster energy transition rewards flexible production more quickly.
Study compares priors for ABNs to improve model accuracy.
problem Inadequate priors lead to model selection issues in ABNs.
method Simulation study with three priors: Gaussian, Student's t, and strongly informative Gaussian.
result Informative Student's t-prior performs best, mitigating Lindley's paradox.
Develops a model to explain price dynamics under predictable market flow.
problem Diffusive price dynamics paradox under predictable market-order flow.
method Integrates square-root price-impact law into Lillo--Mike--Farmer model.
result Price dynamics are diffusive at long times under predictable market-order flow.
Pachner move 3 ->3 deals with triangulations of four-dimensional manifolds. We present an algebraic relation corresponding in a natural way to this move and based, a bit paradoxically, on three-dimensional geometry.
The paper identifies conditions for trend reversal in classification tasks.
problem Trend reversal in classification scores and dataset values.
method Algebraic conditions and numerical results for ridge regression.
result Existence of pathological regularization regimes for certain dataset conditions.
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalizat…
The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with…
CPDOs can't achieve a Cash-In event in finite tosses, mirroring Zeno's Paradox.
problem The impossibility of achieving a Cash-In event in CPDOs, mirroring Zeno's Paradox.
method Coin-tossing model and analysis of infinite geometric series.
result CPDOs can't achieve a Cash-In event in a finite lifetime, mirroring Zeno's Paradox.
Paper proposes a new DR estimator for adaptive experiments with improved performance.
problem Improving policy evaluation in adaptive experiments with dependent samples.
method Adaptive-fitting variant of sample-splitting for non-Donsker nuisance estimators.
result Proposed DR estimator shows better performance than other estimators with dependent samples.
Introduces hierarchical uncertainty using U-sequences.
problem Tackles Ellsberg's paradox in multi-layer uncertainty.
method Uses category theory to construct U-sequences and endofunctors.
result Constructs a universal uncertainty space for multi-layer uncertainty.
Aggregated variables can mask causal effects, turning unconfounded into confounded relations.
problem Aggregated variables can mask causal effects, leading to paradoxical confounding.
method Analysis of how aggregated variables can change the definition of causality and the feasibility of causal relations.
result Macro causal relations are defined by micro states, not just aggregated variables.
The 2008 financial crisis revealed banking consolidation paradoxically increased systemic fragility and global financial contagion with negligible spatial decay.
problem Fundamental vulnerabilities in interconnected banking systems during the 2008 financial crisis were inadequately addressed by existing frameworks.
method Developed a unified spatial-network framework using spectral analysis of network Laplacian operators combined with spatial difference-in-differences identification.
result Banking consolidation paradoxically increased systemic fragility and global financial contagion with negligible spatial decay.
Study analyzes neural network models to understand generalization performance.
problem Understanding good generalization in neural networks.
method Analyzed a corpus of models from a public contest, breaking ALPHAHAT into scale and shape metrics.
result Identified a Simpson's paradox in metric performance across different model depths and regularization hyperparameters.
The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts, empirical evidence paradoxically do not show that most individual stoc…
Paper uses bond pricing and convexity adjustments to explain herd immunity paradox.
problem Early onset of herd immunity contradicts R value estimates from early stage growth.
method Utilizes Vasicek's bond pricing formula and de Finetti's Theorem approach.
result Reduces modeling discrepancy to simple convexity formulas.
We solve the paradox of score-based methods by minimizing path variance.
problem Score-based methods are path-dependent, leading to inaccurate and unstable estimators.
method Propose MVP Principle to minimize path variance, derive closed-form expression, and use flexible Kumaraswamy Mixture Model.
result Establishes new state-of-the-art results on challenging benchmarks.
The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-v…