Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T13:27:18.025Z Has data issue: false hasContentIssue false
  • English
  • Français

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; ogawa-s@se.ritsumei.ac.jp
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; pontier@lsp.ups-tlse.fr
Get access

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 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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amendinger, J., Martingale representation theorems for initially enlarged filtrations. Stoch. Proc. Appl. 89 (2000) 101–116. CrossRef
Amendinger, J., Imkeller, P. and Schweizer, M., Additional logarithmic utility of an insider. Stoch. Proc. Appl. 75 (1998) 263–286. CrossRef
Back, K., Insider trading in continuous time. Rev. Financial Stud. 5 (1992) 387–409. CrossRef
B. Biais, T. Mariotti, G. Plantin and J.C. Rochet, Dynamic security design. Rev. Economic Stud. to appear.
Cho, K.H. and Karoui, N. EL, Insider trading and nonlinear equilibria:uniqueness: single auction case. Annales d'économie et de statistique 60 (2000) 21–41. CrossRef
Cho, K.H., Continuous auctions and insider trading: uniqueness and risk aversion. Finance and Stochastics 7 (2003) 47–71. CrossRef
M. Chaleyat-Maurel and T. Jeulin, Grossissement gaussien de la filtration brownienne, in Séminaire de Calcul Stochastique 1982-83, Paris, Lect. Notes Math. 1118 (1985) 59–109.
N. El Karoui, Les aspects probabilistes du contrôle stochastique, in Ecole d'été de Saint Flour 1979, Lect. Notes Math. 872 (1981) 73–238.
Föllmer, H. and Imkeller, P., Anticipation cancelled by a Girsanov transformation: a paradox on Wiener space. Ann. Inst. Henri Poincaré 29 (1993) 569–586.
W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control. Springer, Berlin (1975).
A. Grorud and M. Pontier, Comment détecter le délit d'initié ? CRAS, Sér. 1 324 (1997) 1137–1142.
A. Grorud and M. Pontier, Insider trading in a continuous time market model. IJTAF. 1 (1998) 331–347.
A. Grorud and M. Pontier, Probabilité neutre au risque et asymétrie d'information. CRAS, Sér. 1 329 (1999) 1009–1014.
A. Grorud and M. Pontier, Asymmetrical information and incomplete markets. IJTAF. 4 (2001) 285–302.
Hillairet, C., Existence of an equilibrium with discontinuous prices, asymmetric information and non trivial initial σ-fields. Math. Finance 15 (2005) 99–117. CrossRef
J. Jacod, Grossissement initial, Hypothèse H' et Théorème de Girsanov, in Séminaire de Calcul Stochastique 1982–83, Paris, Lect. Notes Math. 1118 (1985) 15–35.
T. Jeulin, Semi-martingales et grossissement de filtration. Springer-Verlag (1980).
Continuous, A.S. Kyle auctions and insider trading. Econometrica 53 (1985) 1315–1335.
Karatzas, I. and Pikovsky, I., Anticipative portfolio optimization. Adv. Appl. Probab. 28 (1996) 1095–1122.
G. Lasserre, Quelques modèles d'équilibre avec asymétrie d'information. Thèse soutenue à l'université de Paris VII, le 16 décembre 2003.
G. Lasserre, Asymmetric information and imperfect competition in a continuous time multivariate security model, Finance and Stochastics 8 (2004) 285–309.
P. Protter, Stochastic Integration and Differential Equations. Springer-Verlag (1990).
Schweizer, M., On the minimal martingale measure and the Föllmer-Schweizer decomposition. Stochastic Anal. Appl. 13 (1995) 573–599. CrossRef
M. Yor, Grossissement de filtrations et absolue continuité de noyaux, in Séminaire de Calcul Stochastique 1982-83, Paris, Lect Notes Math. 1118 (1985) 6–14.