Mathematisches Seminar

Vortrag von Prof. Dr. Christoph Kühn (Universität Frankfurt): "Price-Setting of Market Makers: A Filtering Problem with an Endogenous Filtration "

14.12.2012 von 14:45 bis 15:30

LMS 4, Raum 424

Vortrag Mini-Workshop, Einladender: Irle

Abstract:

Market makers provide liquidity by offering to buy or to sell the respective asset at any time. They quote a bid price at which they commit themselves to buy and a higher ask price at which they sell.

We study the price-setting problem of market makers under risk neutrality and perfect competition in continuous time. Thereby we follow the classic Glosten-Milgrom model (1985) that defines bid and ask prices as expectations of a true value of the asset given the market makers’ partial information that includes the customers trading decisions. The true value is modeled as a Markov process that can be observed by the customers with some noise at Poisson times.

We analyze the price-setting problem by solving a filtering problem with an endogenous filtration that depends on the bid and ask price process quoted by the market maker. Under some conditions we show existence and uniqueness of the price processes. However, it turns out that in the standard textbook example with perfect insiders and pure noise traders dynamic uniqueness fails to hold although the static bid and ask prices are unique (joint work with Matthias Riedel).

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