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

Optimal brokerage contracts in Almgren-Chriss model with multiple clients