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PRICE SETTING OF MARKET MAKERS: A FILTERING PROBLEM WITH ENDOGENOUS FILTRATION
Author(s) -
Kühn Christoph,
Riedel Matthias
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12079
Subject(s) - bid price , ask price , economics , market maker , bid–ask spread , asset (computer security) , microeconomics , mid price , risk neutral measure , econometrics , endogeneity , market price , markov process , uniqueness , mathematical economics , price level , computer science , market liquidity , mathematics , finance , paleontology , mathematical analysis , statistics , computer security , horse , stock market , biology , keynesian economics
This paper studies the price‐setting problem of market makers under risk neutrality and perfect competition in continuous time. The classic approach of Glosten–Milgrom is followed. Bid and ask prices are defined as conditional 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. A mathematically rigorous analysis of the price‐setting problem is carried out, solving a filtering problem with endogenous filtration that depends on the bid and ask price processes quoted by the market maker. The existence and uniqueness of the bid and ask price processes is shown under some conditions.