# Equilibres sur un marché financier avec asymétrie d'information et discontinuité des prix

Abstract : The aim of this thesis is to study the existence of an equilibrium on a financial market with discontinous prices and asymmetric information. In the first part, we solve the optimization problem of an initial strong insider, who knows from the beginning a functional of the price process. Under an additional assumption of independence of filtrations, we give a necessary and sufficient condition for the existence of an equilibrium defined by the consumption market clearing condition. We show that when it reaches an equilibrium, the market reveals all relevant information. In the second part, we study two other modelizations of side information. The first one is the progressive strong information: the side information is perturbed by an independent noise changing throughout time. The second one is the weak information: the insider anticipates the law of a random variable that will be realized at a future date. From a mathematical point of vue, the enlargement of filtration techniques are irrelevant in this latter case (contrary to a strong information) and a minimal probability measure'' summarizes this side information. Then we study the formation of an equilibrium with insiders having different side information. We focus our attention on the portfolio market clearing condition. We show that the more informed an agent is, the less weight he must have in the financial market, in order to achieve an equilibrium. In the last part, we simulate the insider's strategy for different examples of side information and we compare it to the optimal strategy of a non-insider. We simulate the formation of an equilibrium and the maximum weight an insider can invest in the market so that an equilibrium could exist.
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https://tel.archives-ouvertes.fr/tel-00008278
Contributor : Caroline Hillairet <>
Submitted on : Thursday, January 27, 2005 - 5:18:54 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:04:16 PM

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• HAL Id : tel-00008278, version 1

### Citation

Caroline Hillairet. Equilibres sur un marché financier avec asymétrie d'information et discontinuité des prix. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2004. Français. ⟨tel-00008278⟩

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