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Point process bridges and weak convergence of insider trading models. (English) Zbl 1284.60096

Summary: 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 the 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 the Kyle-Back equilibrium, without the additional assumptions imposed by K. Back and S. Baruch [Econometrica 72, No. 2, 433–465 (2004; Zbl 1130.91328)], when the common intensity of the Poisson processes tends to infinity.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F05 Central limit and other weak theorems
91B26 Auctions, bargaining, bidding and selling, and other market models

Citations:

Zbl 1130.91328
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