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Pricing rules under asymmetric information

Published online by Cambridge University Press:  01 March 2007

Shigeyoshi Ogawa  and
Monique Pontier
Shigeyoshi Ogawa
Affiliation:
Department of Mathematical Sciences Ritsumeikan University, Kusatsu, Shiga, 525-8577 Japan; [email protected]
Monique Pontier
Affiliation:
U.M.R. CNRS C 5583, Laboratoire de statistique et probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France; [email protected]
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Abstract

We consider an extension of the Kyle and Back's model [Back, Rev. Finance Stud.5 (1992) 387–409; Kyle, Econometrica35 (1985) 1315–1335],meaning a model for the market with a continuous time risky assetand asymmetrical information. There are threefinancial agents: the market maker, an insider trader (who knows a randomvariable V which will be revealed at final time) and a non informed agent. Here we assume thatthe non informed agent is strategic, namely he/she uses a utility function to optimize his/her strategy.Optimal control theory is applied to obtain a pricing ruleand to prove the existenceof an equilibrium price when the insider trader and the non informedagent are risk-neutral. We will show that if such an equilibrium exists, then the non informed agent's optimal strategy is to do nothing, in other words to be non strategic.

Keywords

Equilibriumoptimal controlasymmetric information.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 80 - 88
Copyright
© EDP Sciences, SMAI, 2007

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