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Finite utility on financial markets with asymmetric information and structure properties of the price dynamics

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  • Mathematics

Abstract

doi:10.1016/j.anihpb.2004.03.008 Ann. I. H. Poincaré – PR 41 (2005) 479–503 www.elsevier.com/locate/anihpb F Abstra We proces which S view S is a s ity gai utility  2005 Résum On lution l’évolu dans la une dé espéré supplé  2005 MSC: p Keywor Sem ✩ Thi * Cor E-m 0246-0 doi:10. inite utility on financial markets with asymmetric information and structure properties of the price dynamics ✩ Stefan Ankirchner, Peter Imkeller ∗ Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany Received 20 November 2003; received in revised form 9 February 2004; accepted 2 March 2004 Available online 25 March 2005 ct consider financial markets with two kinds of small traders: regular traders who perceive the (continuous) asset price s S through its natural filtration, and insiders who possess some information advantage which makes the filtrations through they experience the evolution of the market richer. We discuss the link between (NFLVR), the semimartingale property of ed from the agent’s perspective, and bounded expected utility. We show that whenever an agent’s expected utility is finite, emimartingale with a Doob–Meyer decomposition featuring a martingale part and an information drift. The expected util- n of an insider with respect to a regular trader is calculated in a completely general setting. In particular, for the logarithmic function, utility gain is a function of the relative information drift alone, regardless of whether the market admits arbitrage. Elsevier SAS. All rights reserved. é considère un marché financier avec deux sortes de petits investisseurs : des investisseurs réguliers qui perçoivent l’évo- du prix S dans sa filtration naturelle, et des agents initiés ayant des informations supplémentaires et qui ainsi suivent tion du prix par une filtration plus riche. On discute le rapport entre (NFLVR), la propriété de semimartingale de S vue perspective de l’agent, et la bornitude de l’espérance de l’utilité. Si cell

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