Dark Markets with Multiple Assets: Segmentation, Asymptotic Stability, and Equilibrium Prices

TL;DR

This paper extends the dark market model to multiple assets with segmentation, proving a unique stable equilibrium and deriving closed-form asset prices, while analyzing how investor interactions influence prices.

Contribution

It introduces a segmented, multi-asset dark market model with a novel stability proof and explicit equilibrium prices, expanding prior single-asset models.

Findings

Unique asymptotically stable equilibrium established

Closed-form solutions for asset prices derived

Equilibrium prices sensitive to investor interaction levels

Abstract

We study a generalization of the model of a dark market due to Duffie-G\^arleanu- Pedersen [6]. Our market is segmented and involves multiple assets. We show that this market has a unique asymptotically stable equilibrium. In order to establish this result, we use a novel approach inspired by a theory due to McKenzie and Hawkins-Simon. Moreover, we obtain a closed form solution for the price of each asset at which investors trade at equilibrium. We conduct a comparative statics analysis which shows, among other sensitivities, how equilibrium prices respond to the level of interactions between investors.