Probabilistic Theory of Stock Exchanges
Шрифт:
So, Fig. 1.1 shows a typical graphic economic model of a market system, or simply, a market. This model, configured by analogy with models for physical multiparticle systems, uses a number of legends or conventions to demonstrate typical market structure.
Fig. 1.1. Graphical model of a single-commodity multiagent market economy in the economic two-dimensional price-quantity space. The dots inside the conventional sphere represent market agents: buyers (green dots) and sellers (red dots), forming demand and supply, respectively. The sphere is divided into two parts by the narrow blue line, which symbolically marks the narrow area of prices, where the transactions in the market are made at the current experimental price pExp. Buyers are in the left hemisphere and sellers are in the right hemisphere, since the buyers’ prices are lower than the sellers’ prices with very rare exceptions.
The main structural element of the model is the market itself, consisting of a certain number of interacting market agents: buyers and sellers. This market is not a closed system – it is an open system, because it is under the constant influence of its institutional and external environment, as well as other markets and other sources of influence. All these factors also serve as structural elements of the market, because they exert a strong influence on market agents, and without taking it into account it is impossible to obtain a reliable description of the mechanisms of market operation and its results.
Further, in order to be able to mathematically describe the dynamics of the economy, we should, just like in physics, place the entire market into some constructed economic spaces. Since such economic spaces, in contrast to the physical space, have an auxiliary and formal character, they can be constructed in different ways depending on the tasks to be solved. In this paper, it is appropriate to use the price-quantity space corresponding to two sets of independent variables, prices P and quantities Q for all traded goods on the market (PQ– space). For clarity, we denote the names of independent variables and their corresponding coordinate axes in bold. Despite its seeming simplicity, the concept of multidimensional economic space introduced in this study is of great importance in theory, since it provides a fundamental opportunity to describe the dynamics of economic systems in mathematical and graphical languages, as it has long been accepted in science.
This paper will extensively use the notion of "market structure", which includes both the agent structure of the market itself and all significant external factors and forces of various nature that affect the operation of the market. The study of the market structure and its various microstructures and the identification of the most important characteristics and connections between them represents the most important purpose of any economic theory.
The approach of probabilistic economics, aimed at solving the problem of adequate quantitative description of each agent’s behavior in the market, as well as the behavior of the market as a whole, is based on one rather simple premise or hypothesis, which we will call an axiom. This axiom, which has a rather general character, forms the basis for the implementation of supply and demand concept in a probabilistic economy.
All market agents are identical, only their supply and demand are different. This axiom is the starting point in building up the theory. It says that in the context of studying the basic or determinant features of the behavior of market agents in the market and the market as a whole, especially in terms of the formation of market prices and trade volumes, all market agents have common or identical properties, depending mainly on the income and expenditure of agents, or, more precisely, on their S&D for the goods and services produced and traded in markets. In other words, all buyers with the same demand are identical, just as all sellers with the same supply are identical. It can also be said that such agents are indistinguishable from the point of view of influencing the outcome of market trading or exchange. This axiom is something similar to the principle of indistinguishability of particles in physics, but, naturally, it is not as strict as the principle of indistinguishability in physics. It is the S&D of agents that primarily determine their economic behavior in markets and, ultimately, the behavior of all markets; they are the only characteristics of agents and the main input data for calculation methods in probabilistic economics, i.e. the parameters that determine the studied economic system.
This axiom points to the possibility of constructing sufficiently generalized and accurate models of the agents’ behavior in the market and, consequently, of the market as a whole on the basis of agents’ supply and demand. It leads us to the right path for determining and defining general properties of the market agents’ behavior, which, in turn, enables us to identify general regularities in the course of market processes. This gives us a reliable basis for building theoretical economic models at a fairly high scientific level, using formal physical and mathematical methods. We are convinced that only these types of general market phenomena and processes fairly represent the main interest of any sufficiently accurate scientific investigation using the methods of theoretical and experimental economics. In other words, this axiom forces us to focus on building the economic theory as a sufficiently rigorous science, based on the study of the behavior of individual agents (see the principle of methodological individualism [Mises, 2005] in terms of their S&D, i.e., behavior determined by their individual demand or supply.
To avoid misunderstandings, let us make the following note. Of course, there are many aspects of the economic agents’ behavior in markets, which are determined by specific nuances and peculiarities in the behavior of particular people and communities in different situations and in different markets, and which often cannot be described in terms of supply and demand. These nuances and peculiarities of specific economic agents in particular markets are important, of course, when studying the process of making specific market decisions in particular situations of planning their market intentions and strategies [Schiller, 2000], for example, when choosing their quotations in course of trading at an exchange, but they are not the subject of probabilistic economics in this study. Moreover, for a probabilistic economics, it is all these nuances and features that determine the supply and demand for each agent at any given time, and these S&D are the inputs to the probabilistic economics. But, again, neither these nuances and peculiarities, nor concepts such as expected utility and risk [Wickens, 2012], are the basic concepts or the subject of research in probabilistic economics. The same is true for the nuances and peculiarities of exchange markets: in probabilistic theory, there is no need to describe and explicitly account for them, unlike in traditional theories like efficient market theory [Fama, 1970]. After all, it is not all these specific nuances and peculiarities of decision-making processes of market agents, and not the properties of specific markets like perfect competition, etc., but the specific actions of market agents and their determining role in the operation, development and evolution of markets, and the economy as a whole, that constitute the main subject of research and the main content of economic theory, in our opinion. As we argued above, it is, of course, important to understand what market agents think, and why they make these particular decisions, and not others, but, nevertheless, this is the subject of research in other more applied disciplines of economic science.
As we know, specific definitions of supply and demand as well as formulations of the S&D concept and methods of building S&D functions differ from each other in each economic theory, depending on its goals, objectives and possibilities. For example, the concept of supply and demand in mainstream neoclassical economics is based on the intentions or action plans of market agents. The intentions or plans of market agents are a trade secret, but it is completely impossible to build up a quantitative economic theory on the basis of the unobservable intentions or plans of real market agents. On the contrary, probabilistic economics is built on the basis of real actions of these agents in markets that can be observed and measured. More precisely, in a probabilistic economics, market S&D are derived or result from real agent S&D, i.e. from real agent market actions. In this fundamental point, by the way, probabilistic economics is close to the Austrian school of economics, especially in the interpretation of Ludwig von Mises [2005]. In other words, unlike, say, neoclassics, the probabilistic functions S&D are determined on the basis of the real actions of market agents in the market. And they are calculated with strict account of the following six principles of probabilistic economic theory.
Probabilistic economics is based on the most well-known concept of economic theory, namely the concept of S&D. In its most general form, this concept is formulated in probabilistic economics as follows: all the main things that happen in the market depend on some specific balance of supply and demand, determined on the basis of decisions made and openly presented in the form of market orders or market quotations to buy or sell a certain amount of an asset at a certain price. And only what is determined in the market by supply and demand, expressed in this form, is the subject of the study of probabilistic economics. In this sense it can also be called S&D economic theory, and the S&D principle itself is the main element of its basis.
This is generally the most important concept, or paradigm, in respect of the markets. Here it is: every market consists of market agents, buyers and sellers, interacting quite intensively, and prone not only to competition, but also to mutually beneficial social cooperation. There are no other market forces in markets, except the forces of market agents’ interaction. All market results are a consequence of the market agents’ actions, even if their actions were strongly influenced by other factors: the state, institutions, etc. Everything that happens in markets is done by interacting market agents and therefore only agent-based models (agent action-based models or below simply action-based models) can provide a reasonable and reliable quantitative basis for any modern economic theory. And the actions of market agents in the market are exactly the issuing of bids or quotations to buy or sell, which was discussed above.