Arbitrage Equilibrium Research Articles

Jaynes machine: The universal microstructure of deep neural networks

Despite the recent stunning progress in large-scale deep neural network applications, our understanding of their microstructure, ‘energy’ functions, and optimal design remains incomplete. Here, we present a new game-theoretic framework, called statistical teleodynamics, that reveals important insights into these key properties. The optimally robust design of such networks inherently involves computational benefit–cost trade-offs that physics-inspired models do not adequately capture. These trade-offs occur as neurons and connections compete to increase their effective utilities under resource constraints during training. In a fully trained network, this results in a state of arbitrage equilibrium, where all neurons in a given layer have the same effective utility, and all connections to a given layer have the same effective utility. The equilibrium is characterized by the emergence of two lognormal distributions of connection weights and neuronal output as the universal microstructure of large deep neural networks. We call such a network the Jaynes Machine. Our theoretical predictions are shown to be supported by empirical data from seven large-scale deep neural networks. We also show that the Hopfield network and the Boltzmann Machine are the same special case of the Jaynes Machine.

Reduced interest option pricing for green bonds

PurposeThis paper originally proposed the fuzzy option pricing method for green bonds. Based on the requirements of arbitrage equilibrium, this paper draws on Merton's corporate bond option pricing model.Design/methodology/approachDescribing the asset value behavior of green bond issuing enterprises through diffusion-jump processes to reflect the uncertainty brought by carbon emission reduction policies and technologies, using approximation methods to get the analytical pricing formula and then, using a fuzzification technique of Choquet expectation under λ-additive fuzzy measures after considering fuzzy factors, the paper provides fuzzy intervals for the parity coupon rates of green bonds with different subjective levels for investors.FindingsThe paper proposes and argues the classical and fuzzy option pricing methods in turn for both corporate ordinary bonds and green bonds, considering carbon risk or climate risk. It implements the scenario analysis varying with industry emission standards and discusses the sensitiveness of the related key parameters of the option.Practical implicationsThe fuzzy option pricing for the green bonds provides the scope of the variable equilibrium values, operational theoretical supports and some policy implications of carbon reduction and promoting green funding.Originality/valueThe logic of introducing the fuzziness of the option pricing for the green bonds lies with considering the existence of fuzzy information about the project supported by the green bond and the subjectivity of investors and it also responds to changes in technological uncertainty and policy uncertainty in the process of “carbon peaking and carbon neutrality.”

Participation of strategic district heating networks in electricity markets: An arbitrage mechanism and its equilibrium analysis

Combined electricity-heat operation improves social welfare compared with the traditional heat-driven operation. However, it is left open how to achieve such an improvement in the current electricity market. Therefore, an arbitrage mechanism enabling strategic district heating networks (DHNs) to participate in electricity markets is designed, which settles the payment concerning the power deviation and the locational marginal price (LMP). Individual interests of both energy sectors are addressed via a bi-level model, while analytical results of the arbitrage equilibrium are proved theoretically. Although the mechanism intends to allow DHNs to profit selfishly from utilizing energy storage, it is strikingly guaranteed that electric power networks also benefit from this. A Pareto improvement is thus achieved by the mechanism with enhanced social welfare efficiency at the arbitrage equilibrium. The proposed mechanism is numerically compared with the traditional heat-driven operation, combined operation and existing cooperative and non-cooperative game approaches, while the merits are verified in two integrated electricity and heat systems with different scales.

Arbitrage Equilibrium, Invariance, and the Emergence of Spontaneous Order in the Dynamics of Bird-like Agents.

The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith's in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems.

A unified theory of emergent equilibrium phenomena in active and passive matter

Recent attempts towards a theory of active matter utilize concepts and methods from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, such approaches typically do not seem to recognize the critical feature of some kinds of active matter (particularly the biological ones), namely, the role of purpose, and the naturally attendant concept of the pursuit of maximum utility, which we believe is the crucial difference between active and passive matter. Here we introduce a novel game-theoretic framework, statistical teleodynamics, that accounts for this feature explicitly and show how it can be integrated with conventional statistical mechanics to develop a unified theory of arbitrage equilibrium in active and passive matter. We propose a spectrum of self-actualizing capabilities, going from none to completely strategic decision-making, and envision the various examples of active matter systems occupying someplace in this spectrum. We show how statistical teleodynamics reduces to familiar results in statistical mechanics in the limit of zero self-actualization. At the other extreme, in an economic setting, it provides novel insights about the emergence of income distributions and their fairness in an ideal free-market society. As examples of agents in between these limits, we show how our theory predicts the behavior of active Brownian particles, the emergence of ant craters, and phase equilibria in social segregation dynamics. We suggest that our theory offers a novel systems theoretic perspective of emergent phenomena that could serve as the starting point for a more comprehensive theory of design, control, and optimization through self-organization.

Occupational arbitrage equilibrium as an entropy maximizing solution

A standard critique of attempts to apply entropy-maximizing perspectives to income distribution phenomena in economics is that they do not have appropriate characterizations of individuals making choices, which is at the core of economic modeling. This paper presents a possible bridge between these two seemingly separate universes of discourse. With a specific illustration we show that a conventional model of choice between occupations by individuals can lead to an economic equilibrium which can also be characterized as an outcome which maximizes the entropy of the distribution of individuals across occupations (and hence across incomes). This occupational choice interpretation can provide economic and institutional basis to what has, up to now, often been characterized as somewhat mechanical translation of methods from one discipline to another, without substantive content. The illustrations provided in the paper are a first step in exploring the possible linkages between occupational choice and maximum entropy approaches in modelling income distribution outcomes.

An Option Pricing Model with Liquidity Adjustment of Underlying Asset

An important assumption of the Black and Scholes option pricing model in 1973 is that underlying stock market liquidity has full liquidity. However, if the liquidity is not sufficient, the behavior of the investors, replicating an option by self financing portfolio, will cause the underlying stock price changes and therefore result in the systematic bias between BS option price and real option price. According to the no arbitrage equilibrium principle, this paper added liquidity premium created by option replication to the geometric Brownian motion of underlying assets, then deduced the liquidity-adjusted generalized option pricing differential equation, and we proved that the equation has a unique analytical solution. Since an explicit analytical solution cannot derived from the liquidity-adjusted generalized option pricing differential equation, the finite difference method is used to solve the numerical solution of the model, and we proved that the numerical solution is stable. Through empirical research on Shanghai 50ETF options market, we find that the numerical solution is more close to the real option price than the BS model.

Arbitrage, Markov Processes, and Asset Price Paths

Recent results have characterized the class of continuous sample path stochastic processes admissible as equilibrium price processes in a frictionless, continuous trading market under a no arbitrage equilibrium. These results are not complete since the role of the Markov assumption, made by all substantive models of security prices, is not made clear. Given this assumption, the characterization results will be meaningful only if there exist inadmissible stochastic processes. This paper shows that, for strongly Markov processes, the inadmissible class is empty. Hence the no-arbitrage equilibrium condition plays no role in the sample path characterizations. This highlights the role of the Markov assumption.

Agricultural arbitrage and risk preferences

A structural intertemporal model of agricultural asset arbitrage equilibrium is developed and applied to agriculture in the North Central region of the US. The data are consistent with a unifying level of risk aversion. The levels of risk aversion are more plausible than previous estimates for agriculture. However, the standard arbitrage equilibrium is rejected; perhaps, this is due to the period and the shortness of the period studied.

When Is Stock Picking Likely to Be Successful? Evidence from Mutual Funds

Consistent with a costly arbitrage equilibrium in which arbitrage costs insulate mispricing, this study finds that mutual fund managers have stock-picking ability for stocks with high idiosyncratic volatility but not for stocks with low idiosyncratic volatility. These findings suggest that fund managers and other investors may want to pay special attention to high-idiosyncratic-volatility stocks because they provide fertile ground for stock picking. The study also finds that the stock-picking ability of the average mutual fund manager declined after the extreme growth in the number of both mutual funds and hedge funds in the late 1990s.

When Is Stock Picking Likely to Be Successful? Evidence from Mutual Funds

Consistent with a costly arbitrage equilibrium in which arbitrage costs insulate mispricing, this study finds that mutual fund managers have stock-picking ability for stocks with high idiosyncratic volatility but not for stocks with low idiosyncratic volatility. These findings suggest that fund managers and other investors may want to pay special attention to high-idiosyncratic-volatility stocks because they provide fertile ground for stock picking. The study also finds that the stock-picking ability of the average mutual fund manager declined after the extreme growth in the number of both mutual funds and hedge funds in the late 1990s.

Bond Indebtedness in a Recursive Dynamic CGE Model

In this paper, we present a minimalist version of a model of bond financing and debt, imbedded in a stepwise dynamic CGE model. The proposed specification takes into account the main characteristics of bond financing. Bonds compete on the securities market with shares, so that the yield demanded by the buyers of new bond issues increases as the cumulative bond debt grows relative to the stock of outstanding shares. Restrictions are imposed on the maturity structure of bonds, so that it is possible to attain a reasonable compromise between a realistic representation of the evolution of the debt, and the demands on model memory of past variables values which impinge on the current period. In the proposed model, the borrowing government reimburses bonds that have reached maturity, and pays interest on the outstanding debt. The prices of bonds issued at different periods and with different maturities are consistent with an arbitrage equilibrium. The supply of new bonds and of new shares is determined by the government's and business's borrowing needs. Security demand reflects the rational choices of portfolio managing households, following a version of the Decaluwe-Souissi model. These notions are illustrated with fictitious data in model EXTER-Debt. The full specification of the model is described, and simulation results are presented which demonstrate model properties.

The true story of wine and cloth, or: building blocks of an evolutionary political economy of international trade

Standard trade theory is a theory about the structure of international production which emerges from an international arbitrage equilibrium. It is not a theory about the activity of trading which is simply taken for granted or which is treated implicitly in the concept of exogenous trade costs. This paper proposes an alternative evolutionary framework based on networks as structures of non-price interactions into which price/quantity-interactions are embedded. These networks manifest different levels with specific problems of coordination and communication, i.e. levels of market transactions, of transaction-enabling transactions, of markets for market access rights, and of the respective transaction-enabling transactions. Furthermore, the theory is based on the analysis of capabilities to trade, resting upon competitive advantage, which cannot be imitated. The exploitation of competitive advantage presupposes the capability to control network interactions, identified as social capital. Finally, the security of market access reflects power balances among countries.

Bond Financing and Debt in a Stepwise Dynamic CGE Model (La dette obligataire dans un MEGC dynamique sequentiel)

In this paper, we present a minimalist version of a model of bond financing and debt, to be imbedded in a stepwise dynamic CGE model. The proposed specification takes into account the following characteristics of bond financing: - bonds are issued at a given date; - they have a given face value; - they bear interest at a rate that is fixed relative to their face value; - they have a fixed maturity date, at which they are reimbursed by the issuer to the holders. Bonds compete on the securities market with shares, so that the yield demanded by the buyers of new bond issues increases as the cumulative bond debt grows relative to the stock of outstanding shares. Restrictions are imposed on the maturity structure of bonds, so that it is possible to attain a reasonable compromise between a realistic representation of the evolution of the debt, and the demands on model memory of past variables values which impinge on the current period. In the proposed model, the borrowing government reimburses bonds that have reached maturity, and pays interest on the outstanding debt. The prices of bonds issued at different periods and with different maturities are consistent with an arbitrage equilibrium. The supply of new bonds and of new shares is determined by the government's and entreprises' borrowing needs. Security demand reflects the rational choices of portfolio managing households, as in the Decaluwe-Souissi model. The model is presented in two versions: a basic model, and a model in which, although there is still no money, the real face value of bonds is eroded as it would due to inflation.

A Contribution to the Theory and Practice of Rational Financial Contracting

This paper presents a theory of corporate finance from the perspective of bondholders. Towards this end an equilibrium model of a debt and equity financed firm is developed that motivates the need for an upfront bond contract that solves an agency problem between bondholders and stockholders. This bond contract guides the firm towards a no arbitrage equilibrium by directing managers to make investment decisions conforming to the risk aversion of their shareholders and then make financing decisions that preserve the investment quality of their bonds. Empirical evidence on the investment and financing of nonfinancial corporations conform to the predictions of the model.

Past Returns and Investment Trust Discounts

Abstract: The relationship between past net asset value returns and the current discount on investment trusts is investigated. The relationship is weaker for the component that is common to all trusts in the same sector, and is significantly stronger for more liquid trusts. The time lag before returns have their full impact on discounts is consistent with the requirements of distinguishing ‘skill’ from noise. Although discounts vary widely even within the same sector, the range of variation appears to be consistent with an arbitrage equilibrium, in which the profits of exploiting apparent pricing anomalies are just insufficient to invite arbitrage trades.

Limited arbitrage in international wheat markets: threshold and smooth transition cointegration

The strength of the adjustment towards arbitrage equilibrium can be expected to be somehow proportional to the extent of market price deviations from equilibrium. In this article, threshold and smooth transition cointegration models are applied to quarterly wheat prices of three major world suppliers over the period 1973–99. Results based on arranged autoregressions of the error term of a static regression do not prove to be robust. Although non‐linear models relying on a multivariate system approach yield partly contradictory results, the main evidence from the latter suggests a weakening, rather than an outright inaction, of the adjustment process in the inner regime.

On the Notion of the Rate of Profit

This paper aims at a clarification of the classical notion of the rate of profit with respect to the process of gravitation towards long period positions. It is demonstrated that some existing definitions of that rate, in particular ‘synchronic’ rates of profit which are based on a revaluation of either the costs of production or of the value of outputs, do not exhibit the relevant feature of a measure for the profitability of a production process as they fail to serve as an indicator for diverting liquid funds from less to more profitable employments. It is argued that all elements of profits or losses including those which result from the expected revaluation of capital or outputs respectively are to be taken into account. Hence the ‘diachronic’ rate of profit is the proper measure which guides the decisions of producers or capitalists to utilise one or another method of production or to withdraw capital from less profitable employments and invest into promising activities. That rate is uniform in any arbitrage equilibrium, and is not a distinguishing characteristic of long-run positions. The definition of the rate of profit is conditional on individual expectations of future prices and is therefore either not operable or is not general.

Arbitrage Equilibrium with Transaction Costs

The general topic of this paper is the transmission of disturbances in asset markets. The specific topic is the role of transaction costs in this transmission. Do high transaction costs shelter a market against foreign disturbances while 'bottling up' domestic disturbances at home? The question is considered in the context of a small-scale general equilibrium model of asset arbitrage with quadratic transaction cost functions. The main conclusion is that the transmission of (disturbances depends more on the relationships between different transaction cost rates than on their absolute level. A progressive decline of transaction costs, therefore, does not necessarily strengthen the transmission of disturbances, nor can artificial increases of transaction costs be relied upon to reduce it. Copyright 1994 by Ohio State University Press.

A Comment on Zoning, Returns to Scale, and the Value of Undeveloped Land

This paper revisits the relationship between land value and parcel size. The authors demonstrate that, using a simple arbitrage equilibrium argument, the value-size relationship is convex (concave) whenever land assembly (subdivision) is possible. They also explore further the impact of zoning on market outcomes. Copyright 1993 by MIT Press.