Abstract: We study a game between liquidity provider and liquidity taker agents interacting in an over-the-counter market, for which the typical example is foreign exchange. We show how a suitable design of parameterized families of reward functions coupled with associated shared policy learning can make populations of deep reinforcement learning driven such agents learn emergent behaviors relative to a wide spectrum of incentives encompassing profit-and-loss, optimal execution and market share, from scratch, simply by playing against each other. In particular, we find that liquidity providers naturally learn to balance hedging and skewing as a function of their incentives, where the latter refers to setting their buy and sell prices asymmetrically as a function of their inventory. We also discuss our RL-based calibration method which we found performed well at imposing constraints on the game equilibrium. Finally, we show how modern game theoretical tools can help analyze our complex market game, namely differentiable games and their potential-Hamiltonian decomposition, as well as present a simple discrete-time order book snapshot model used in our simulator, which continuous-time limit displays quadratic variance and generalizes existing work.

Bio: Nelson is a research director in the AI Research team at J.P. Morgan, New York. His research interests include game theory, multi-agent reinforcement learning and mathematical finance. He has recently been working on the modeling and calibration of over-the-counter markets using multi-agent RL, and on the topic of learning to converge to Nash equilibria in games as a function of their nature. His work has been published in academic venues including NeurIPS, ACM Intl. Conference on AI in Finance, SIAM Journal on Financial Mathematics, Random Operators and Stochastic Equations, or Stochastic Analysis and Applications. Previously, he worked as a rates exotics quant at J.P. Morgan, rates strats at Morgan Stanley, and quant at Deloitte. Nelson graduated in mathematical finance from CentraleSupelec and Columbia University, and received his PhD in applied mathematics from the University of Calgary.

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