Financial equilibrium with asymmetric information and random horizon

Çetin, Umut ORCID: 0000-0001-8905-853X (2018) Financial equilibrium with asymmetric information and random horizon. Finance and Stochastics, 22 (1). pp. 97-126. ISSN 0949-2984

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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.

Item Type:	Article
Official URL:	https://link.springer.com/journal/780
Additional Information:	© 2017 The Author © CC BY 4.0
Divisions:	Statistics
Subjects:	H Social Sciences > HG Finance
Date Deposited:	06 Oct 2017 12:58
Last Modified:	11 Dec 2024 21:31
URI:	http://eprints.lse.ac.uk/id/eprint/84495

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