Abstract
The objective of this essay is to bring to the attention of mathematicians of finance the field of market micro-structure and the issues raised by the design of trading markets in presence of asymmetric information. In the first part of the essay we present a synthesis of several papers which analyse trading volume and price formation in presence of informed and uninformed traders as well as noise traders: Grossman and Stiglitz (1980) where agents are competitive, Kyle (1985) where the informed agent is strategic, and Rochet and Vila (1994) where convex analysis techniques are used to show that a variant of the Kyle (1985) equilibrium is the solution of a market mechanism design problem. In the second part of this essay, we present the case where there is no noise trading and trading endogenously stems from risk sharing as well as informational motivations as in Glosten (1989). Our reformulation of the analysis of Glosten (1989) illustrates that variation calculus and convex analysis provide a simple and powerful way to deal with the rather difficult problems raised by the design of market mechanisms.
Paper prepared for the third 1996 session of the Centro Internazionale Matematico Estivo, on Financial Mathematics. Many thanks to Rose Anne Dana, Nicole El Karoui, Vincent Lacoste and participants at the CIME session for helpful comments. We were also influenced by numerous discussions with David Martimort. The usual disclaimer applies.
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Biais, B., Rochet, J.C. (1997). Risk sharing, adverse selection and market structure. In: Runggaldier, W.J. (eds) Financial Mathematics. Lecture Notes in Mathematics, vol 1656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091998
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DOI: https://doi.org/10.1007/BFb0091998
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