Pricing rules under asymmetric information
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 80-88

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.

DOI : 10.1051/ps:2007007
Classification : 49N30, 60H10, 93E20
Keywords: equilibrium, optimal control, asymmetric information 
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Ogawa, Shigeyoshi; Pontier, Monique. Pricing rules under asymmetric information. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 80-88. doi: 10.1051/ps:2007007

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