Distributive justice and allocation by the market: On the characterisation of a fair market economy

After critically examining different notions of fairness in allocating goods and leisure in an economy with production, the paper considers an alternative approach to distributive justice and discusses the concept of a fair market economy (EAFME).     

Explaining shopping behavior in a market economy country: A short-term mathematical model applied to the case of Spain

In recent decades, pathological consumption has become a growing behavioral misbehavior. Impulsive consumption is governed by two internal behavioral mechanisms that respond fundamentally to the hedonism or Pascal effect and to the emulation or Veblen effect. Today's development of technology acts as a catalyst of consumption by increasing access and availability to products, as well as the advertisement impact. This paper presents a compartmental discrete matrix mathematical model that allows short-term estimates of ordinary, impulsive, and pathological buyers in Spain in three different economic scenarios. The results show that impulsive and pathological buyers will increase in all the economic scenarios. Notable differences in the number of ordinary buyers are found for the group aged over 65 years.     

A model for speculation in a dynamic economy

The paper deals with speculation strategies in a dynamic economy, where “speculation” means participating in a market with the intention to gain a reward by first buying an item and thereafter selling it at a possibly higher price. By assuming that the states of the economy form a Markov chain the problem is modeled as a discrete time Markov decision process. The optimal strategies (which are pairs of stopping times) are identified. Under quite general conditions the optimal rule for the selling process turns out to be a control limit policy in both state of economy and time. Techniques for the computation of optimal strategies are presented; some numerical examples are also discussed. For a static economy closed-form solutions are given     

Stability analysis of a cobweb model with market interactions

This paper explores the steady-state properties and the dynamic behavior of a generalization of the classical cobweb model. Under fairly general demand and cost functions, producers form naïve expectations about future prices and select their output so as to maximize expected profits. Unlike the traditional setup, producers have the choice between two markets, and tend to enter that which was more profitable in the recent past. Such a switching process implies time-varying aggregated supply schedules, thus representing a further source of nonlinearity for the dynamics of prices. Analytical investigations and the numerical simulation of a particular case with linear demand and supply indicate that such interactions may destabilize otherwise stable markets and generate complex dynamics.     

Nonlinear effects in a discrete-time dynamic model of a stock market

The time evolution of prices and savings in a stock market is modeled by a discrete time nonlinear dynamical system. The model proposed has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear effects acting out of the equilibrium. The nonlinearities strongly influence the kind of long-run dynamics of the system. In particular, the global geometric properties of the noninvertible map of the plane, whose iteration gives the evolution of the system, are important to understand the global bifurcations which change the qualitative properties of the asymptotic dynamics. Such global bifurcations are studied by geometric and numerical methods based on the theory of critical curves, a powerful tool for the characterization of the global dynamical properties of noninvertible mappings of the plane. The model unfolds more complex chaotic and unpredictable trajectories as a consequence of increasing agents' “speculative” or “capital gain realizing” attitudes. The global analysis indicates that, for some ranges of the parameter values, the system has several coexisting attractors, and it may not be robust with respect to exogenous shocks due to the complexity of the basins of attraction.     

A differential game model of a market of substitutable products

Modern industrial organization often classifies groups of differentiated products that are fairly good substitutes to belong to the same market. This paper develops a differential game model of a market of substitutable products. To avoid the problem of time-inconsistency, we solve a feedback Nash equilibrium solution for the game. A set of state-dependent equilibrium strategies is derived. Extensions of the model to a stochastic formulation and to an infinite time horizon specification are also provided.     

Quantile Hedging in a semi-static market with model uncertainty

With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test, an arbitrage-free discretization of the market is proposed as an approximation. The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and helps numerical calculation of the quantile hedging price. As the discretization becomes finer, the approximate quantile hedging price converges and the hedging strategy is asymptotically optimal in the original market.     

The danger model: application to a competitive market

The behavior of the firm in a competitive market based on the idea of the human system, i.e., using a danger activator and a defence system, is modelled. The proposed model uses three variables: market share ratio, danger index and the ratio of relative investment between the firm and the total investments including the competition. The danger activator, the defence and the market reaction functions, which explain how the danger index becomes activated, how the firm reacts to a danger signal, and the market reaction to the firm’s actions, respectively, are carefully constructed. This leads to a parametric dynamic system that governs the behavior of the competitive market. The following five classical behaviors of a firm result: monopoly, below aimed market share, aimed market share, above aimed market share and out of market. Formulas for a sensitivity analysis are derived to determine how and how much the equilibrium points of the dynamic system change when the parameters change. All the concepts are illustrated by graphs that show the equilibrium points and the trajectories of the system.     

American option prices in a Markov chain market model

This paper is a sequel to our previous paper ‘A New Paradigm in Asset Pricing’ in which we construct a model for asset pricing in a world where the randomness is modeled by a Markov chain. In this paper we develop a theory of optimal stopping and related variational inequalities for American options in this model. A version of Saigal's Lemma is established and numerical results obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

A behavioral stock market model

Stock exchanges are modeled as nonlinear closed-loop systems where the plant dynamics is defined by known stock market regulations and the actions of agents are based on their beliefs and behavior. The decision of the agents may contain a random element, thus we get a nonlinear stochastic feedback system. The market is in equilibrium when the actions of the agents reinforce their beliefs on the price dynamics. Assuming that linear predictors are used for prediction of the price process, a stochastic approximation procedure for finding market equilibrium is described. The proposed procedure is analyzed using the theory of Benveniste et al. (Adaptive algorithms and stochastic approximations. Springer, Berlin, 1990). A simulation result is also presented.     

A mathematical model of market competition

We consider a mathematical model of decision making by a company attempting to win a market share. We assume that the company releases its products to the market under the competitive conditions that another company is making similar products. Both companies can vary the kinds of their products on the market as well as the prices in accordance with consumer preferences. Each company aims to maximize its profit. A mathematical statement of the decision-making problem for the market players is a bilevel mathematical programming problem that reduces to a competitive facility location problem. As regards the latter, we propose a method for finding an upper bound for the optimal value of the objective function and an algorithm for constructing an approximate solution. The algorithm amounts to local ascent search in a neighborhood of a particular form, which starts with an initial approximate solution obtained simultaneously with an upper bound. We give a computational example of the problem under study which demonstrates the output of the algorithm.     

General financial market model defined by a liquidation value process

Financial market models defined by a liquidation value process generalize the conic models of Schachermayer and Kabanov where the transaction costs are proportional to the exchanged volumes of traded assets. The solvency set of all portfolio positions that can be liquidated without any debt is not necessary convex, e.g. in presence of proportional transaction costs and fixed costs. Therefore, the classical duality principle based on the Hahn–Banach separation theorem is not appropriate to characterize the prices super hedging a contingent claim. Using an alternative method based on the concepts of essential supremum and maximum, we provide a characterization of European and American contingent claim prices under the absence of arbitrage opportunity of the second kind.     

Symmetry breaking in a bull and bear financial market model

We investigate bifurcation structures in the parameter space of a one-dimensional piecewise linear map with two discontinuity points. This map describes endogenous bull and bear market dynamics arising from a simple asset-pricing model. An important feature of our model is that some speculators only enter the market if the price is sufficiently distant to its fundamental value. Our analysis starts with the investigation of a particular case in which the map is symmetric with respect to the origin, associated with equal market entry thresholds in the bull and bear market. We then generalize our analysis by exploring how novel bifurcation structures may emerge when the map’s symmetry is broken.     

Price manipulation in a market impact model with dark pool

For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren–Chriss model. Conditions for the absence of price manipulation for all Almgren–Chriss models include the absence of temporary cross-venue impact, the presence of full permanent cross-venue impact and the additional penalization of orders executed in the dark pool. When a particular Almgren–Chriss model has been fixed, we show by a number of examples that the regularity of the dark-pool model hinges in a subtle way on the interplay of all model parameters and on the liquidation time constraint. The paper can also be seen as a case study for the regularity of market impact models in general.     

Pure equilibria in a simple dynamic model of strategic market game

We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful properties, such as Lipschitz property and symmetry. We also show value of the game to be nondecreasing both in state and discount factor. Further, for some values of discount factor, exact form of optimal strategies is found. For β less than , there is an equilibrium such that players make large bids. For β close to 1, there is an equilibrium with small bids. Similar result is obtained for the long run average reward game.     

Criticality and punctuated equilibrium in a spin system model of a financial market

Recent works on self-organised criticality (SOC) in pulse coupled relaxation oscillators have shown SOC to be related to frustrated attempts of the system to synchronise. Criticality has also been connected to punctuated equilibrium behaviour. We describe a model which shows a non-equilibrium phase transition and seems to link these two ideas. Near the transition, punctuated equilibrium behaviour is seen, with avalanches occurring on all scales. This scaling is described by an exponent very near 1.     

Special modes in a two-sector economy model with an integral utility function

In this work, we study a two-sector economic model with the Cobb–Douglas production function on an infinite planning horizon where the utility function is a functional of an integral form and a Lagrangian of a logarithmic type. A one-dimensional equation is obtained that depends only on the coefficients of elasticity and amortization, and determines the possible special modes. The special modes are described in analytical form.