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EDSR et EDSPR avec grossissement de filtration, problèmes d'asymétrie d'information et de couverture sur les marchés financiers

Abstract : The subject of this PhD Thesis is the study of existence and uniqueness of the solution of backward stochastic differential equations, under an initial enlargement of filtration. This mathematical problem was motivated by a financial problem of hedging for an insider trader, who has an additional information on the market. In a first part, we solve the problem, successively in a continuous framework and in a model with jumps, and we prove, under hypothesis (H3) on the enlargement of filtration, thanks to a martingale representation theorem, that the BSDE in the enlarged space, has a unique solution under standard hypotheses on the driver. One of the main consequences is that in a complete market, having an additional information does not provide additional hedging strategies. In a second part, we develop a model of informed and influent agent, which leads to a problem of solving a forward-backward SDE under an enlarged filtration, and we obtain an existence and uniqueness theorem. We deal also with the problem of hedging in an incomplete market, where incompleteness is due to incomplete information. In the last part, we generalize the results of the first part to BSDEs with random terminal time.
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https://tel.archives-ouvertes.fr/tel-00450944
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Submitted on : Wednesday, January 27, 2010 - 4:58:38 PM
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Anne Eyraud-Loisel. EDSR et EDSPR avec grossissement de filtration, problèmes d'asymétrie d'information et de couverture sur les marchés financiers. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2005. Français. ⟨tel-00450944⟩

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