Competition in Dealer Markets with Internalisation and Externalisation

Battle Count: 92

Highly relevant for understanding dealer market dynamics, optimal market making strategies, and the impact of competing liquidity providers on execution costs. The closed-form Nash equilibrium provides actionable insights for algorithmic trading firms operating as market makers. The prisoner's dilemma finding (internalisers forced to externalise) has direct implications for FX and fixed income trading desks. The model quantifies how dealer composition affects client execution costs.

The theoretical framework involves solving a (5N+2)-dimensional FBSDE system via matrix exponentials and linear algebra. Implementation requires constructing large matrices K, T, H_V, H_X of dimension (5N+2)x(5N+2) and (4N+1)x(5N+2) respectively. The closed-form solution (Theorem 2.4) requires matrix inversion at each time step. Numerical simulation of Poisson processes, price impact dynamics, and inventory tracking adds further complexity. The epsilon-Nash equilibrium test (Remark 3.1) requires extensive Monte Carlo simulation.

The paper provides full mathematical derivations, explicit parameter values (Table 1), and detailed model specifications. However, no code or data repository is mentioned. The numerical experiments use 1000 simulated paths with specified parameters, making replication feasible but requiring significant implementation effort. The matrix definitions in Appendices B and C are fully specified.