arXiv research

Paper provides a rigorous proof of the index theorem for economists.

Unified theory explains market impact using a simplified supply-demand parameter.

The paper calculates how fast optimal investment strategies approach CRRA strategies in stochastic factor models.

Recently we reported on an application of the Tsallis non-extensive statistics to the S&P500 stock index. There we argued that the statistics are applicable to a broad range of markets and exchanges where anamolous (super) diffusion and 'heavy' tails of the distribution are present, as they are in the S&P500. We have c…

In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presented. In computing eq…

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account t…

We propose a frustrated and disordered many-body model of a stockmarket in which independent adaptive traders can trade a stock subject to the economic law of supply and demand. We show that the typical scaling properties and the correlated volatility arise as a consequence of the collective behavior of agents: With th…

In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of t…

Extends return extrapolation to nonlinear, asymmetric functions under stochastic volatility.

In standard Walrasian auctions, the price of a good is defined as the point where the supply and demand curves intersect. Since both curves are generically regular, the response to small perturbations is linearly small. However, a crucial ingredient is absent of the theory, namely transactions themselves. What happens …

We extend return extrapolation to incorporate asymmetry and saturation, finding that asymmetric nonlinear extrapolation leads to lower welfare loss.

MQTransformer improves forecast accuracy with context-aware attention.

Study develops smart contract framework for procurement under demand variability.

A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behaviors are observed for the return variance $σ^2$, the price impact $H$ and the predictability $K$ for both models with linear and square root impact functions. The sum of the traders' wealth displays a positive v…

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a singl…

We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…

Demand functions for goods are generally cyclical in nature with characteristics such as trend or stochasticity. Most existing demand forecasting techniques in literature are designed to manage and forecast this type of demand functions. However, if the demand function is lumpy in nature, then the general demand foreca…

A new formula reveals symmetries between mean excess and ES functions.

Paper introduces privacy-preserving inventory policy learning for feature-based newsvendor with unknown demand.

In recent years, dock-less shared bikes have been widely spread across many cities in China and facilitate people's lives. However, at the same time, it also raises many problems about dock-less shared bike management due to the mismatching between demands and real distribution of bikes. Before deploying dock-less shar…

We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via agents' excess demand functions, and the diffusion approximation approach is appl…

Implementing a set of microeconomic criteria, we develop price dynamics equations using a function of demand/supply with key symmetry properties. The function of demand/supply can be linear or nonlinear. The type of function determines the nature of the tail of the distribution based on the randomness in the supply and…

Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated as Lagrangians. Assumptions of integrability of Lagrangians and dynamics are im…

Deep learning model reduces food waste by stabilizing online food delivery supply chains.

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde)that exhibit transitio…

Study excess capacity in neural networks using Rademacher complexity.

The paper bounds the excess risk of deep neural networks for weakly dependent processes.

Study excess risk in statistical inference with transformations.

Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for modelling stochastic interactions between agents, based on a herding process corrected b…

Transport demand is highly dependent on supply, especially for shared transport services where availability is often limited. As observed demand cannot be higher than available supply, historical transport data typically represents a biased, or censored, version of the true underlying demand pattern. Without explicitly…

We consider a firm that sells products over $T$ periods without knowing the demand function. The firm sequentially sets prices to earn revenue and to learn the underlying demand function simultaneously. A natural heuristic for this problem, commonly used in practice, is greedy iterative least squares (GILS). At each ti…

Optimizes gradual reduction of excess carbon emissions to net-zero.

The paper addresses uncertainty in demand prediction for dynamic pricing.

Exchanges acquire excess processing capacity to accommodate trading activity surges associated with zero-sum high-frequency trader (HFT) "duels." The idle capacity's opportunity cost is an externality of low-latency trading. We build a model of decentralized exchanges (DEX) with flexible capacity. On DEX, HFTs acquire …

Mathematical study of excess growth rate connects info theory with finance.

In a market with stochastic investment opportunities, we study an optimal consumption investment problem for an agent with recursive utility of Epstein-Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize…

New method estimates model risk without knowing function class.

In statistical learning theory, convex surrogates of the 0-1 loss are highly preferred because of the computational and theoretical virtues that convexity brings in. This is of more importance if we consider smooth surrogates as witnessed by the fact that the smoothness is further beneficial both computationally- by at…

This research improves demand forecasting by predicting complete probability density functions using machine learning.

While the investors' responses to price changes and their price forecasts are well accepted major factors contributing to large price fluctuations in financial markets, our study shows that investors' heterogeneous and dynamic risk aversion (DRA) preferences may play a more critical role in the dynamics of asset price …

We prove that a metric measure space $(X,d,m)$ satisfying finite dimensional lower Ricci curvature bounds and whose Sobolev space $W^{1,2}$ is Hilbert is rectifiable. That is, a $RCD^*(K,N)$-space is rectifiable, and in particular for $m$-a.e. point the tangent cone is unique and euclidean of dimension at most $N$. The…

We study a simple exchange model in which price is fixed and the amount of a good transferred between actors depends only on the actors' respective budgets and the existence of a link between transacting actors. The model induces a simply-connected but possibly multi-component bipartite graph. A trading session on a fi…

The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…

In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between trend-following and contrarian actions that generates the price chaos, and give par…

This paper develops a pricing model for data assets from the buyer's perspective.

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size n. The bounds lead us to consider sample variance penalization, a nov…

New method refines model-free evaluation of complex machine learning models.

This paper compares AMMs and LOBs in exchange mechanisms, formalizing complexity vs. expressiveness trade-offs.