On uniqueness of equilibrium in the Kyle model
type: Item
instance of: scholarly article
title: On uniqueness of equilibrium in the Kyle model
zbMATH Open document ID: 1367.91205
author: Andrew McLennan
author: Paulo Monteiro
author: R. Tourky
published in: Mathematics and Financial Economics
publication date: 2017-03-07T00:00:00Z
full work available at URL: http://hdl.handle.net/10438/13028
review text: The authors consider optimal trading for an informed investor in the Kyle model. It is assumed that the informed investor has knowledge of the true value of a firm, \(V\). The market maker observes the demand from the informed investor, \(D\), and of an uninformed one, \(U\). In the equilibrium the profit of the market maker is equal to zero. The problem of the informed investor is to find the best response function \(D=\phi(V)\) which maximizes his profit. The value of the firm and the demand of the uninformed investor are assumed to be independent normal variables: \(V\sim N(\mu, \sigma^2_V)\), \(U\sim N(0, \sigma^2_U)\). This problem was already considered in the literature and it was shown that in the class of affine functions the best response is \(\varphi(V) = (V-\mu)\sqrt{\sigma^2_U/\sigma^2_V}\). The authors of the article show that the same result holds for a broader class of response functions. In particular, the main result states that if the equilibrium best-response function \(\phi\) is an analytic function of an open connected interval that has maximal analytic extension, then it is an affine function.
reviewed by: Paweł Kliber
Mathematics Subject Classification ID: 91G99
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 6692618
zbMATH Keywords: Kyle model
zbMATH Keywords: informed trader
zbMATH Keywords: analytic functions
zbMATH Keywords: optimal trading
MaRDI profile type: Publication
OpenAlex ID: W1559470931
cites work: On the aggregation of information in competitive markets
cites work: Q4945855
cites work: Continuous Auctions and Insider Trading
cites work: Sliced Inverse Regression for Dimension Reduction
cites work: Basic Complex Analysis
DOI: 10.1007/S11579-016-0175-7
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description: scientific article; zbMATH DE number 6692618