Nous développons un modèle basé agents pour reproduire deux anomalies fréquemment observées sur les marchés financiers : distribution leptokurtique des rendements et ampleur de la volatilité irrégulière mais persistante de ces mêmes rendements. Notre but est de montrer de façon probante que ces anomalies pourraient être attribuées à une formation mimétique des anticipations des intervenants sur les marchés. Nous nous éloignons des développements récents dans le domaine des modèles modèles basés agents en finance pour proposer un modèle très simple, estimé à partir des traits statistiques saillants de l’indice français journalier CAC 40. L’hypothèse d’anticipations mimétiques peut ainsi être testée : elle n’est pas rejetée dans notre modélisation. / We develop an agent-based model to replicate two frequently observed anomalies in the financial markets: the fat tails and the clustered volatility of the distribution of the returns. Our goal is to show conclusively that these anomalies could be attributed to a mimetic formation of the expectations of the stakeholders in the markets. We did not follow the rencent developpments in the field of the ACE model in the finance, but we propose a very simple model which is estimated from the stylized facts of the French daily index CAC 40. The hypothesis of mimetic anticipations can thus be tested: it is not rejected in our modeling.

Darwinian Evolutionary system - a system satisfying the abstract conditions: reproduction with heritable variation, in a finite world, giving rise to Natural Selection encompasses a complex and subtle system of interrelated theories, whose substantive transplantation to any artificial medium let it be mathematical model or computational model - will be very far from easy. There are two motives in bringing Darwinian evolution into computational frameworks: one to understand the Darwinian evolution, and the other is to view Darwinian evolution - that carries out controlled adaptive-stochastic search in the space of all possible DNA-sequences for emergence and improvement of the living beings on our planet - as an optimization process, which can be simulated in appropriate frameworks to solve some intractable problems. The first motive led to emerging field of study commonly referred to as Artificial Life, and other gave way to emergence of Evolutionary Computation, which is speculated to be the only practical path to the development of ontogenetic machine intelligence. In this thesis we touch upon all the above aspects. Natural selection is the central concept of Darwinian evolution and hence capturing natural selection in computational frameworks which maintains the spirit of Darwinian evolution in the sense of conventional, terrestrial and biological perspectives is essential. Naive models of evolution define natural selection as a process which brings in differential reproductive capabilities in organisms of a population, and hence, most of the evolutionary simulations in Artificial Life and Evolutionary Computation implement selection by differential reproduction: the Attest members of the population are reproduced preferentially at the expense of the less fit members of the population. Formal models in evolutionary biology often subdivide selection into components called 'episodes of selection' to capture the different complex mechanisms of nature by which Darwinian evolution can occur. In this thesis we introduce the concept of 'episodes of selection' into computational frameworks of Darwinian evolution by means of A Conceptual Evolutionary model (ACE-model). ACE-model is proposed to be simple and yet it captures the essential features of modern evolutionary perspectives in evolutionary computation framework. ACE-model is rich enough to offer abstract and structural framework for evolutionary computation and can serve as a basic model for evolutionary algorithms. It captures selection in two episodes in two phases of evolutionary cycle and it offers various parameters by which evolutionary algorithms can control selection mechanisms. In this thesis we propose two evolutionary algorithms namely Malthus evolutionary algorithms and Malthus Spencer evolutionary algorithms based on the ACE-model and we discuss the relevance of parameters offered by ACE-model by simulation studies. As an application of ACE-model to artificial life we study misconceptions involved in defining fitness in evolutionary biology, and we also discuss the importance of introducing fitness landscape in the theories of Darwinian evolution. Another important and independent contribution of this thesis is: A Mathematical Abstraction of Evolutionary process. Evolutionary process is characterized by Evolutionary Criteria and Evolutionary Mechanism which are formalized by classical mathematical tools. Even though the model is in its premature stage to develop any theory based on it, we develop convergence criteria of evolutionary process based on this model.