Search results for: Alexander Saichev
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The set of mechanisms that we have considered up to now explains quite well both ends of the distribution of firm’s sizes. Indeed, while the average growth rate of firm’s asset values, the intensity of firm’s births and the hazard rate of a firm’s sudden death accurately explain the behavior of the population of large firms, the introduction of a lower threshold below which firms disappear (by lack...
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Many theoretical models neglect the possibility that firms disappear. However, firms do not continuously grow. They undergo transient periods of decay that are sometimes persistent and then surrender to their decline which may ultimately lead to their exit from business. Referring as in Chap. 2 to Bonaccorsi Di Patti and Dell’Ariccia (2004), the yearly rate of death of Italian firms is, on average,...
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One of the broadly accepted universal laws of complex systems, particularly relevant in social sciences and economics, is that proposed by Zipf (1949). Zipf’s law usually refers to the fact that the probability P(s) = Pr{S > s} that the value S of some stochastic variable, usually a size or frequency, is greater than s, decays with the growth of s as P(s) ∼ s − 1. This in turn means...
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In all previous chapters, we have studied the steady-state mean density g(s) given by (3.18) of firm’s asset values and its properties, for a stationary intensity ν of firm’s births. In real life, ν is not constant, with periods of strong growth, such as during “new economy bubbles” (Galbraith, 1997; Kindleberger, 2000; Shefrin, 2000; Shiller, 2000; Shleifer, 2000; Sornette, 2003; White, 1996) or...
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The introduction of a mechanism in which firms die introduces already a deviation from Gibrat’s law for small s-values. Killing firms upon first touching the level s 1 > 0 actually means that the corresponding firm’s asset values S(t) do not obey strictly Gibrat’s law of proportionate growth. Indeed, when S(t) becomes close to s 1, the possibility of touching s 1 arises,...
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In the previous chapter, we introduced the mean density of firm’s asset values (3.18), taking into account the flow of firm’s births {t i }. We provided a preliminary analysis of the properties of the mean density of firm sizes. In order to understand more deeply the roots of the power laws (3.24) and (3.25), and at the same time the basis of Zipf’s law (3.27) and...
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This chapter discuss the properties of the realization-dependent density of firm’s sizes. We put together the different ingredients introduced in the previous chapters to analyze the extent to which the mean density of firm’s sizes, which has been the main topic of this book, is representative of the realized density of firm’s sizes in a given economy (i.e., a single realization).
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In this chapter, we describe in detail the continuous version of Gibrat’s law and explain its close connection with the geometric Brownian motion (GBM), underlying any scale independent stochastic process. Due to the importance of the GBM for many economical, physical, biological and sociological applications, we focus our attention on the basic key properties of GBM. Some more subtle statistical...
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The failure of the approach based solely on Gibrat’s principle stems, at least in part, from the fact that it attempts to derive the distribution of firm sizes directly from the distribution of the asset value of a single firm. Indeed, many models start with the implicit or explicit assumption that the set of firms under consideration was born at the same origin of time. This approach is equivalent...
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There are a priori two exit mechanisms for firms: Firms disappear when their asset values become smaller than some minimum level. This is based on the standard idea, justified by the existence of a minimum efficient size, that there is a minimum firm size below which the firm cannot exist. This idea has been considered in several models of firm growth (see, e.g., de Wit, 2005 and references therein)...
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Journal of Economic Behavior and Organization > 2015 > 112 > Complete > 289-310
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which fundamentalist and chartist traders co-exist. Fundamentalists form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to their allocation on the risky asset versus the risk-free asset. Chartists are subjected...
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The European Physical Journal B > 2013 > 86 > 4 > 1-19
Many natural and social systems are characterized by bursty dynamics, for which past events trigger future activity. These systems can be modelled by so-called self-excited Hawkes conditional Poisson processes. It is generally assumed that all events have similar triggering abilities. However, some systems exhibit heterogeneity and clusters with possibly different intra- and inter-triggering, which...
