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Popular understandings of the financial crisis tend to focus on the rents extracted by elite personnel in the financial sector. Professional discussions, however, have addressed the faulty assumptions underlying theory and practice – in particular, the assumption that returns to financial assets follow the Gaussian distribution, in the face of much empirical evidence that these have power law distributions with far higher kurtosis. It turns out that the power law tails of returns to financial assets are also a feature of the distribution of company rates of profit, a discovery that stems from proposals to ‘dissolve’ the traditional transformation problem by abandoning the condition of a uniform rate of profit and instead considering its distribution.Marx himself was aware of the importance of considering the distributional properties of economic variables, based on his reading of Quetelet. In fact, heavy-tailed distributions characterise a wide range of variables in capitalist economies, the best-known probably being the Paretian tail component in distributions of income and wealth. Nor is this simply an empirical fact – such distributions emerge readily from a range of agent-based simulations.Capitalist economies are, in a particular technical sense, complex self-organising systems perpetually on the brink of crisis. This modern understanding is prefigured in Marx’s discussion of how the compulsive character of social relations emerges from the atomistic exercise of human free will in commercial society. The developing literature of probabilistic Marxism successfully applies these insights to the wider fields of econophysics and complexity, demonstrating the continuing relevance of Marx’s thought.

Certain elements of Hayek’s work are prominent precursors to the modern field of complex adaptive systems, including his ideas on spontaneous order, his focus on market processes, his contrast between designing and gardening, and his own framing of complex systems. Conceptually, he was well ahead of his time, prescient in his formulation of novel ways to think about economies and societies. Technically, the fact that he did not mathematically formalize most of the notions he developed makes his insights hard to incorporate unambiguously into models. However, because so much of his work is divorced from the simplistic models proffered by early mathematical economics, it stands as fertile ground for complex systems researchers today. I suggest that Austrian economists can create a progressive research program by building models of these Hayekian ideas, and thereby gain traction within the economics profession. Instead of mathematical models the suite of techniques and tools known as agent-based computing seems particularly well-suited to addressing traditional Austrian topics like money, business cycles, coordination, market processes, and so on, while staying faithful to the methodological individualism and bottom-up perspective that underpin the entire school of thought.

The Truncated Levy Flight (TLF) model has been successfully used to model the return distribution of stock markets in developed economies and a few developing economies such as India. Our primary purpose is to use the TLF to model the S&P 500 and the firms operating in the Ghana Stock Exchange (GSE).

We assess the predictive efficacy of the TLF model by comparing a simulation of the Standard and Poor's 500 (S&P 500) index and that of firms in the stock market in Ghana, using data from the same time period (June 2007–September 2013).

We find that the Levy models relatively accurately models the return distributions of the S&P 500 but does not accurately model the return distributions of firms in the Ghana stock market.

A major limitation is that we examined stock market data only from Ghana, while there are over 29 other African stock markets. We suggest that doctoral students and faculty can compare these stock markets either on the basis of age or the number of firms listed. For example, the oldest stock market was set up in 1883 in Egypt, while the more recent ones were set up in 2012 in the Seychelles and in Somalia.

Scholarly inquiry about the stock markets in Africa represents a rich area of research that we will encourage doctoral students and faculty to go into.

There has been little research done regarding the TLF model and African stock markets and this research has much utility and high level of originality.

The purpose of this chapter is to study the mathematisation of finance – excessive use of mathematical models in finance – which has been widely blamed for the recent financial and economic crisis. We argue that the problem might actually be the financialisation of mathematics, as evidenced by the gradual embedding of branches of mathematics into financial economics. The concept of embeddedness, originally proposed by Polanyi, is relevant to describe the sociological relationship between fields of knowledge. After exploring the relationship between mathematics, finance and economics since antiquity, we find that theoretical developments in the 1950s and 1970s lead directly to this embedding. The key implication of our findings is the realization that it has become necessary to disembed mathematics from finance and economics, and proposes a number of partial steps to facilitate this process. This chapter contributes to the debate on the mathematisation of finance by uniquely combining a historical approach, which chronicles the evolution of the relation between mathematics and finance, with a sociological approach from the perspective of Polyani’s concept of embedding.

Standard financial risk management practices proved unable to provide an adequate understanding and a timely warning of the financial crisis. In particular, the theoretical foundations of risk management and the statistical calibration of risk models are called into question. Policy makers and practitioners respond by looking for new analytical approaches and tools to identify and address new sources of financial risk. Financial markets satisfy reasonable criteria of being considered complex adaptive systems, characterized by complex financial instruments and complex interactions among market actors. Policy makers and practitioners need to take both a micro and macro view of financial risk, identify proper transparency requirements on complex instruments, develop dynamic models of information generation that best approximate observed financial outcomes, and identify and address the causes and consequences of systemic risk. Complexity analysis can make a useful contribution. However, the methodological suitability of complexity theory for financial systems and by extension for risk management is still debatable. Alternative models drawn from the natural sciences and evolutionary theory are proposed.

The chapter dwells on barriers for restoration and development of country's infrastructure on the platform of individual physical and practical forces, which are peculiar for the states with developing and transitional economy, as well as for developed countries. Directions of formation of the organizational model of restoration and development of country's infrastructure on the platform of individual physical and practical forces are presented; forms of public–private partnership are studied, as well as possibilities of financing. An important aspect is finding the mechanisms of leveling the risks according to the given classification. A mechanism of organizational model of controlling development of country's infrastructure and its structural elements are provided.

Political economies evolve institutionally and technologically over time. This means that to understand evolutionary political economy one must understand the nature of the evolutionary process in its full complexity. From the time of Darwin and Spencer natural selection has been seen as the foundation of evolution. This view has remained even as views of how evolution operates more broadly have changed. An issue that some have viewed as an aspect of evolution that natural selection may not fully explain is that of emergence of higher order structures, with this aspect having been associated with the idea of emergence. In recent decades it has been argued that self-organization dynamics may explain such emergence, with this being argued to be constrained, if not overshadowed, by natural selection. Just as the balance between these aspects is debated within organic evolutionary theory, it also arises in the evolution of political economy, as between such examples of self-organizing emergence as the Mengerian analysis of the appearance of commodity money in primitive societies and the natural selection that operates in the competition between firms in markets.

Speculative bubbles have been occurring periodically in local or global real-estate markets and are considered a potential cause of economic crises. In this context, the detection of explosive behaviors in the financial market and the implementation of early warning diagnosis tests are of critical importance. The recent increase in Brazilian housing prices has risen concerns that the Brazilian economy may have a speculative housing bubble. In the present chapter, we employ a recently proposed recursive unit root test in order to identify possible speculative bubbles in data from the Brazilian residential real-estate market. The empirical results show evidence for speculative price bubbles both in Rio de Janeiro and São Paulo, the two main Brazilian cities.