Financial equilibrium with asymmetric information and random horizon

Umut Çetin

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We study in detail and explicitly solve the version of Kyle’s model introduced in a specific case in [2], where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the analysis of time-homogeneous equilibria using tools from the theory of one-dimensional diffusions. It turns out that such an equilibrium is only possible if the final payoff is Bernoulli distributed as in [2]. We show in the second part that the signal of the market makers use in the general case is a time-changed version of the one that they would have used had the final payoff had a Bernoulli distribution. In both cases we characterise explicitly the equilibrium price process and the optimal strategy of the informed trader. Contrary to the original Kyle model it is found that the reciprocal of market’s depth, i.e. Kyle’s lambda, is a uniformly integrable supermartingale. While Kyle’s lambda is a potential, i.e. converges to 0, for the Bernoulli distributed final payoff, its limit in general is different than 0.

Keywords: Kyle's model; financial equilibrium; one-dimensional diffusion; h-transform; potential theory (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2018-01-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Published in Finance and Stochastics, 1, January, 2018, 22(1), pp. 97-126. ISSN: 0949-2984

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