Optimal Market Making in Prediction Markets

Prediction markets are attracting growing attention as trading volumes rise and their practical relevance increases. To ensure efficient price discovery, liquidity provision becomes ever more important. Due to the binary settlement structure in prediction markets, optimal market making leads to an optimization problem that is fundamentally different from the ones studied in classical settings. In this paper, we develop a stochastic control framework for prediction markets in which the market price is modeled as a conditional probability of the outcome that is generated by a transformed latent belief diffusion. A market maker selects bid and ask quotes to maximize expected terminal wealth while controlling both mark-to-market inventory risk and the settlement risk of remaining positions at resolution. We derive the associated Hamilton--Jacobi--Bellman equation and characterize the unique optimal bid and ask quotes. By transforming the equation to the latent belief space and using a fixed-point argument, we prove existence and uniqueness of a classical solution and verify the resulting optimal quoting strategy. In addition, we provide a numerical analysis, which reveals how optimal liquidity provision in prediction markets depends on inventory, market beliefs, time to resolution, and risk aversion. Further, we demonstrate that the optimal quoting strategy substantially improves downside protection while preserving most of its expected profit relative to a myopic benchmark that maximizes the instantaneous expected mark-to-market profit.