Optimal brokerage contracts in Almgren-Chriss model with multiple clients

TL;DR

This paper develops a model for optimal brokerage contracts with multiple heterogeneous clients in an Almgren-Chriss framework, allowing strategic client selection and endogenous reservation values, with practical computational methods and numerical insights.

Contribution

It introduces a novel framework for broker-client interactions with endogenous reservation values and strategic client selection in the Almgren-Chriss model.

Findings

Optimal client portfolios can be characterized computationally.

Client portfolios and profits depend on price impact coefficients.

Numerical experiments illustrate strategic client selection effects.

Abstract

This paper constructs optimal brokerage contracts for multiple (heterogeneous) clients trading a single asset whose price follows the Almgren-Chriss model. The distinctive features of this work are as follows: (i) the reservation values of the clients are determined endogenously, and (ii) the broker is allowed to not offer a contract to some of the potential clients, thus choosing her portfolio of clients strategically. We find a computationally tractable characterization of the optimal portfolios of clients (up to a digital optimization problem, which can be solved efficiently if the number of potential clients is small) and conduct numerical experiments which illustrate how these portfolios, as well as the equilibrium profits of all market participants, depend on the price impact coefficients.