Exponential wealth distribution: a new approach from functional iteration theory

Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In statistical physics, it is obtained from the principle of maximum entropy. In the same context, it can also be derived without any consideration about information theory, only from geometrical arguments under the hypothesis of equiprobability in phase space. Also, several multi-agent economic models based on mappings, with random, deterministic or chaotic interactions, can give rise to the asymptotic appearance of the exponential wealth distribution. An alternative approach to this problem in the framework of iterations in the space of distributions has been recently presented. Concretely, the new iteration given by $f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$. It is found that the exponential distribution is a stable fixed point of the former functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.Comment: 6 pages, 5 figure

From Heterogeneous expectations to exchange rate dynamic:

The purpose of this paper is to analyze how heterogeneous behaviors of agents influence the exchange rates dynamic in the short and long terms. We examine how agents use the information and which kind of information, in order to take theirs decisions to form an expectation of the exchange rate. We investigate a methodology based on interactive agents simulations, following the Santa Fe Artificial Stock Market. Each trader is modeled as an autonomous, interactive agent and the aggregation of their behavior results in foreign exchange market dynamic. Genetic algorithm is the tool used to compute agents, and the simulated market tends to replicate the real EUR/USD exchange rate market. We consider six kinds of agents with pure behavior: fundamentalists, positive feedback traders and negative ones, naive traders, news traders (positive and negative). To reproduce stylized facts of the exchange rates dynamic, we conclude that the key factor is the correct proportion of each agents type, whiteout any need of mimetic behaviors, adaptive agents or pure noisy agentsexchange rates dynamic, heterogeneous interactive agents behaviour, genetic algorithm, learning process

Exponential wealth distribution in a random market. A rigorous explanation

In simulations of some economic gas-like models, the asymptotic regime shows an exponential wealth distribution, independently of the initial wealth distribution given to the system. The appearance of this statistical equilibrium for this type of gas-like models is explained in a rigorous analytical way.Comment: 9 pages, 4 figure

The shadow in the balance sheet: The spectre of Enron and how accountants use the past as a psychological defence against the future

Accounting frameworks play a crucial role in enabling us to make sense of business. These frameworks provide a common language for individuals, organizations and broader economic groupings to understand and make decisions about the commercial realm in which they operate. From a psychodynamic perspective, the language of accounting also plays an important role. On the one hand it offers a way to tame the uncertainty and unknowability of the future by representing it in the same comforting terms as it does the past, thus reducing anxiety. Accounting provides a ‘shorthand’, which achieves a balance between positive and negative, debit and credit, asset and liability. On the other hand, accounting can also provide an arena in which fantasies about the future can be staged. However, the use of accounting language is problematic, particularly when it comes to dealing with the future. First, accounting frameworks are inherently backward looking and second, the reassuring sense of clarity and predictability they give are bought at the price of unrealistic simplification. The shadow is never far away and is a constant source of surprises in the unfolding future of a business. Rationalizing and sanitizing the shadow through accounting language may alleviate anxiety but fails to provide an escape from its effects, and echoes from the shadow side of business are capable of shaking the world in the form of accounting scandals. Governments and businesses have reacted to scandals such as Enron and Worldcom by tightening legislation and refining accounting standards but little, if anything, has been done to bring us any closer to confronting the shadow of business where these scandals have their r

Geometry of Financial Markets -- Towards Information Theory Model of Markets

Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the object of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset X (i.e. in units of X) are given by linear maps. Among various types of metrics that have financial interpretation, the min-max metrics on the space of quotations can be introduced. This metrics has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metrics on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.Comment: Talk given at the APFA5 Conference, Torino, 200