# Pricing rules under asymmetric information

Shigeyoshi Ogawa; Monique Pontier

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 80-88
- ISSN: 1292-8100

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topOgawa, Shigeyoshi, and Pontier, Monique. "Pricing rules under asymmetric information." ESAIM: Probability and Statistics 11 (2007): 80-88. <http://eudml.org/doc/250105>.

@article{Ogawa2007,

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. },

author = {Ogawa, Shigeyoshi, Pontier, Monique},

journal = {ESAIM: Probability and Statistics},

keywords = {Equilibrium; optimal control; asymmetric information.; equilibrium; asymmetric information},

language = {eng},

month = {3},

pages = {80-88},

publisher = {EDP Sciences},

title = {Pricing rules under asymmetric information},

url = {http://eudml.org/doc/250105},

volume = {11},

year = {2007},

}

TY - JOUR

AU - Ogawa, Shigeyoshi

AU - Pontier, Monique

TI - Pricing rules under asymmetric information

JO - ESAIM: Probability and Statistics

DA - 2007/3//

PB - EDP Sciences

VL - 11

SP - 80

EP - 88

AB - 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.

LA - eng

KW - Equilibrium; optimal control; asymmetric information.; equilibrium; asymmetric information

UR - http://eudml.org/doc/250105

ER -

## References

top- J. Amendinger, Martingale representation theorems for initially enlarged filtrations. Stoch. Proc. Appl.89 (2000) 101–116. Zbl1045.60038
- J. Amendinger, P. Imkeller and M. Schweizer, Additional logarithmic utility of an insider. Stoch. Proc. Appl.75 (1998) 263–286. Zbl0934.91020
- K. Back, Insider trading in continuous time. Rev. Financial Stud.5 (1992) 387–409.
- B. Biais, T. Mariotti, G. Plantin and J.C. Rochet, Dynamic security design. Rev. Economic Stud. to appear. Zbl1297.91135
- K.H. Cho and N. EL Karoui, Insider trading and nonlinear equilibria:uniqueness: single auction case. Annales d'économie et de statistique60 (2000) 21–41.
- K.H. Cho, Continuous auctions and insider trading: uniqueness and risk aversion. Finance and Stochastics7 (2003) 47–71. Zbl1066.91057
- 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. Zbl0575.60046
- N. El Karoui, Les aspects probabilistes du contrôle stochastique, in Ecole d'été de Saint Flour 1979, Lect. Notes Math.872 (1981) 73–238.
- H. Föllmer and P. Imkeller, Anticipation cancelled by a Girsanov transformation: a paradox on Wiener space. Ann. Inst. Henri Poincaré29 (1993) 569–586. Zbl0796.60082
- 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. 1324 (1997) 1137–1142.
- A. Grorud and M. Pontier, Insider trading in a continuous time market model. IJTAF. 1 (1998) 331–347. Zbl0909.90023
- A. Grorud and M. Pontier, Probabilité neutre au risque et asymétrie d'information. CRAS, Sér. 1329 (1999) 1009–1014.
- A. Grorud and M. Pontier, Asymmetrical information and incomplete markets. IJTAF. 4 (2001) 285–302. Zbl1154.91542
- C. Hillairet, Existence of an equilibrium with discontinuous prices, asymmetric information and non trivial initial σ-fields. Math. Finance15 (2005) 99–117. Zbl1109.91026
- 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). Zbl0444.60002
- A.S. Kyle, Continuous auctions and insider trading. Econometrica53 (1985) 1315–1335. Zbl0571.90010
- I. Karatzas and I. Pikovsky, Anticipative portfolio optimization. Adv. Appl. Probab.28 (1996) 1095–1122. Zbl0867.90013
- 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 Stochastics8 (2004) 285–309. Zbl1060.91092
- P. Protter, Stochastic Integration and Differential Equations. Springer-Verlag (1990). Zbl0694.60047
- M. Schweizer, On the minimal martingale measure and the Föllmer-Schweizer decomposition. Stochastic Anal. Appl.13 (1995) 573–599. Zbl0837.60042
- 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. Zbl0576.60038

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