Pricing rules under asymmetric information

¹ 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

Accepted: September 2005

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.