Mean‐field games with differing beliefs for algorithmic trading

Even when confronted with the same data, agents often disagree on a model of the real world. Here, we address the question of how interacting heterogeneous agents, who disagree on what model the real world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where each agents performance criteria are computed under a different probability measure. We analyze the mean‐field game (MFG) limit of the stochastic game and show that the Nash equilibrium is given by the solution to a nonstandard vector‐valued forward–backward stochastic differential equation. Under some mild assumptions, we construct the solution in terms of expectations of the filtered states. Furthermore, we prove that the MFG strategy forms an ε‐Nash equilibrium for the finite player game. Finally, we present a least square Monte Carlo based algorithm for computing the equilibria and show through simulations that increasing disagreement may increase price volatility and trading activity.     

Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation

The mean‐variance formulation by Markowitz in the 1950s paved a foundation for modern portfolio selection analysis in a single period. This paper considers an analytical optimal solution to the mean‐variance formulation in multiperiod portfolio selection. Specifically, analytical optimal portfolio policy and analytical expression of the mean‐variance efficient frontier are derived in this paper for the multiperiod mean‐variance formulation. An efficient algorithm is also proposed for finding an optimal portfolio policy to maximize a utility function of the expected value and the variance of the terminal wealth.     

Mean‐variance efficiency of the market portfolio and futures trading

We derived an intertemporal capital asset pricing model in which the mean‐variance efficiency of the market portfolio is neither a necessary nor a sufficient condition. We obtained this result by modeling a frictionless, continuously open financial market in which nonredundant futures contracts are available for trade, in addition to cash assets. Introducing such contracts modifies the way investors optimally allocate their wealth. Their portfolios then comprise the riskless asset, a perturbed mean‐variance‐efficient portfolio of cash assets, and a perturbed mean‐variance‐efficient portfolio of futures contracts. Furthermore, a (3 + K) mutual fund separation is obtained, with K being the number of economic state variables, in lieu of the usual (2 + K) fund separation. Mean‐variance efficiency of the market portfolio is a necessary condition only when cash assets are the sole traded assets. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:329–346, 2001     

Mean–field moral hazard for optimal energy demand response management

We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a continuum of consumers with mean–field interaction, whose consumption is impacted by a common noise. We formulate the problem as a Principal–Agent problem with moral hazard in which the Principal—she—is an electricity producer who observes continuously the consumption of a continuum of risk‐averse consumers, and designs contracts in order to reduce her production costs. More precisely, the producer incentivizes each consumer to reduce the average and the volatility of his consumption in different usages, without observing the efforts he makes. We prove that the producer can benefit from considering the continuum of consumers by indexing contracts on the consumption of one Agent and aggregate consumption statistics from the distribution of the entire population of consumers. In the case of linear energy valuation, we provide closed‐form expression for this new type of optimal contracts that maximizes the utility of the producer. In most cases, we show that this new type of contracts allows the Principal to choose the risks she wants to bear, and to reduce the problem at hand to an uncorrelated one.     

A Quasi‐Analytical Pricing Model for Arithmetic Asian Options

We develop a quasi‐analytical pricing method for discretely sampled arithmetic Asian options. We derive an asymptotic approximation of the arithmetic average with the geometric average of lognormal variables. Numerical experiments show that the asymptotic approximation is accurate and the absolute error converges very quickly as the number of observations increases. The absolute error is of the order of 10^?5 to 10^?6 for daily average. We then derive quasi‐analytical formulas for arithmetic Asian options under the Black–Scholes framework, in which the probability density of the geometric average is used. Extensive experiments are conducted to compare the proposed method with the various existing semianalytical methods. The overall accuracy of the proposed method is better than any other methods tested. The proposed method performs much better than the second best one for at‐the‐money Asian options under high volatility. The mean pricing error of the proposed method for a daily average Asian option is 37.5% less than the second best one. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:1143–1166, 2013     

Counter‐Credit‐Risk Yield Spreads: A Puzzle in China's Corporate Bond Market

In this paper, using China's risk‐free and corporate zero yields together with aggregate credit risk measures and various control variables from 2006 to 2013, we document a puzzle of counter‐credit‐risk corporate yield spreads. We interpret this puzzle as a symptom of the immaturity of China's credit bond market, which reveals a distorted pricing mechanism latent in the fundamental of this market. We also find interesting results about relationships between corporate yield spreads and interest rates and risk premia and the stock index, and these results are somewhat attributed to this puzzle.     

A Personality‐Competence Model of Opinion Leadership

Opinion leaders constitute a central consumer segment for targeted marketing strategies. By separating opinion leadership into a generalized and domain‐specific component, this study examines the psychological profile of N = 417 consumers from Germany and incorporates opinion leadership into a hierarchical framework of human personality. Results emphasize two major sources of domain‐specific opinion leadership (DSOL): personality in the form of a general, domain‐independent influencer trait and competencies in terms of product‐specific knowledge. Moreover, the study highlights a number of traits including the Big Five of personality, typical intellectual engagement, and general self‐efficacy that form a distinct personality profile of DSOL. The effects of these personality traits on DSOL are partially mediated by generalized opinion leadership and objective knowledge.     

A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges

The no‐arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long‐memory features of the range‐based volatility estimators are analyzed, and fractional cointegration is tested in a semi‐parametric framework. In particular, the no‐arbitrage condition is used to derive a long‐run relationship between volatility measures and to justify the use of a fractional vector error correction model (FVECM) to study their dynamic relationship. The out‐of‐sample forecasting superiority of FVECM, with respect to alternative models, is documented. The results highlight the importance of incorporating the long‐run equilibrium in volatilities to obtain better forecasts, given the information content in the volatility of futures prices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:77–102, 2013     

Norm Bounds and A Homographic Approximation for the Wage–Profit Curve

This paper provides lower and upper norm bounds for the wage–profit curve in linear single‐product systems. Thus, it also constructs an algebraically simple (i.e. homographic) and empirically powerful approximation to that curve. The results finally suggest that actual economies tend to behave as ‘corn‐tractor’ systems with respect to the shape of the wage–profit curve and, at the same time, behave as three‐industry systems with respect to the shape of the production price–profit rate curves.     

A Simulation Model Of Multi‐Echelon Retail Inventory With Cross‐Channel Product Returns

This study explores the relationship between a retailer's product returns processing structure and Multi‐Echelon inventory system performance under cross‐channel and same‐channel product returns policies with nonstationary demand. Our research contributes to the growing body of reverse logistics literature, offering insight into how a retailer's logistical returns management strategy can impact inventory effectiveness in cross‐channel retail environments. Adopting a contingency framework, we develop research hypotheses which we test through experimentation on a Multi‐Echelon retail inventory system within a discrete‐event simulation. Model parameters are derived from data collected from a large U.S. retailer of consumer durable and nondurable goods. We find an amplifying effect of a cross‐channel returns policy on the positive relationship between a decentralized returns processing structure and inventory effectiveness. Further, through our analysis of nonstationarity in demand and resulting returns, we uncover strong main and interaction effects that seasonal demand variation can have on inventory outcomes, even under only moderate levels of seasonality. Our results highlight the need for firms to align logistical structures for returns processing with the returns policy and the external environment, while also lending credence to calls within the logistics literature for improved modeling of nonstationary demand in inventory management research.     

Cross‐Country Determinants of Early‐Stage Necessity and Opportunity‐Motivated Entrepreneurship: Accounting for Model Uncertainty

Model uncertainty is one of the most pervasive challenges in the social sciences. Cross‐country studies in entrepreneurship have largely ignored this issue. In this paper, we evaluate the robustness of 44 possible determinants of early‐stage opportunity‐motivated entrepreneurship (OME) and necessity‐motivated entrepreneurship (NME) that are broadly classified in four groups: (1) economic variables, (2) formal institutions, (3) cultural values, and (4) legal origins and geography. The results, which are based on a representative world sample of up to 73 countries, suggest that institutional variables associated with the principles of economic freedom are most robustly correlated with OME and NME. Our findings also identify net income inequality and Scandinavian legal origins as weakly robust predictors of both types of entrepreneurial activity. Furthermore, we find that log GDP per capita is only a weakly robust predictor of NME, but not OME. We discuss implications for future research.     

Distribution Channel Relational Cohesion Exchange Model: A Small‐to‐Medium Enterprise Manufacturer's Perspective

This study investigated the influence of dealers' expert, referent, and legitimate sources of power on small‐to‐medium enterprise manufacturers' relationship commitment in distribution channel systems. A theoretical model drawing on the relational cohesion theory and the extant marketing literature is developed and tested empirically using a sample data set of 452 from Zimbabwe. In this model, expert, referent, and legitimate powers are the predictors, whereas trust, cooperation, and relationship satisfaction are the mediators, and relationship commitment is the outcome variable. Analysis reveals that these three powers positively influence the mediators and outcome variable in a significant way, except for legitimate power to cooperation relationship. Managerial implications and future studies are suggested.     

Redistribution in a Neo‐Kaleckian Two‐country Model

We investigate the interaction between demand‐driven growth and income distribution in open economies, by combining expenditure‐switching and demand spillover effects in a neo‐Kaleckian two country model. First, we specify elasticities of wage share and real exchange rate to the money wage relative to labor productivity, in order to precisely describe the distributive pass‐through from money wages to the labor share and the real exchange rate. Second, we analyze the demand effects of an increase in the money wage for given labor productivity (a redistribution towards labor) in both Home and Foreign country, as well as globally. We derive closed form results for two identical countries. These results indicate that redistribution towards labor at Home: (i) always increases growth globally if Home is wage‐led, but can lead to lower growth at Home relative to Foreign; and (ii) will always imply lower growth at Home relative to Foreign if Home is profit‐led, but can still be growth‐enhancing at Home. Thus, to the extent that countries are concerned with their relative economic performance, a fallacy of composition can emerge. Numerical simulations suggest that these fallacies could indeed occur. As a consequence, ‘returns to coordination’ over international labor policies might be substantial.     

A Model of motivated cognition to account for the link between self‐monitoring and materialism

Drawing on previous theorizing about the development of materialistic values, a model of motivated cognition is proposed to account for the positive association between self‐monitoring and materialism. The model suggests that self‐monitoring is associated with individual differences in belonging motivation, that belonging motivation shapes people's beliefs about buying as a means of belonging within valued groups, and that buying‐is‐for‐belonging beliefs shape the degree to which people value wealth and luxury. Results from two studies supported this model and suggested that the self‐monitoring results are not better attributed to extraversion, social self‐confidence, or shyness. The proposed model emphasizes that traits associated with a strong need to belong may predispose people toward materialism. © 2007 Wiley Periodicals, Inc.