Document ESAIM: P&S, February 2007, Vol. 11, pp. 80-88
DOI: 10.1051/ps:2007007
Pricing rules under asymmetric information
Shigeyoshi Ogawa1 and Monique Pontier21 Department of Mathematical Sciences Ritsumeikan University, Kusatsu, Shiga, 525-8577 Japan; ogawa-s@se.ritsumei.ac.jp
2 U.M.R. CNRS C 5583, Laboratoire de statistique et probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France; pontier@lsp.ups-tlse.fr
(Invited paper accepted September 2005. Published online 1 March 2007.)
Abstract
We consider an extension of the Kyle and Back's model [Back, Rev. Finance Stud. 5 (1992) 387-409; Kyle, Econometrica 35 (1985) 1315-1335],
meaning a model for the market with a continuous time risky asset
and asymmetrical information. There are three
financial agents: the market maker, an insider trader (who knows a random
variable V which will be revealed at final time) and a non informed
agent. Here we assume that
the 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 rule
and to prove the existence
of an equilibrium price when the insider trader and the non informed
agent 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.
Mathematics Subject Classification. 49N30, 60H10, 93E20.
Key words: Equilibrium, optimal control, asymmetric information.
© EDP Sciences, SMAI 2007