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2013 Point process bridges and weak convergence of insider trading models
Umut Cetin, Hao Xing
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Electron. J. Probab. 18: 1-24 (2013). DOI: 10.1214/EJP.v18-2039


We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time $1$ value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the insider employs a mixed strategy to randomly submit two types of orders: one type trades in the same direction as noise trades while the other cancels some of the noise trades by submitting opposite orders when noise trades arrive. The construction also allows us to prove that Glosten-Milgrom equilibria converge weakly to Kyle-Back equilibrium, without the additional assumptions imposed in <em>K. Back and S. Baruch, Econometrica, 72 (2004), pp. 433-465</em>, when the common intensity of the Poisson processes tends to infinity.


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Umut Cetin. Hao Xing. "Point process bridges and weak convergence of insider trading models." Electron. J. Probab. 18 1 - 24, 2013.


Accepted: 17 February 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60096
MathSciNet: MR3035754
Digital Object Identifier: 10.1214/EJP.v18-2039

Primary: 60G55
Secondary: 60F05 , 91G80

Keywords: Equilibrium , Glosten-Milgrom model , insider trading , Kyle model , point process bridge , weak convergence

Vol.18 • 2013
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