Optimal Market Making in Prediction Markets

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Directly addresses optimal market making strategy in prediction markets, which are increasingly important financial venues (Kalshi, Polymarket with billions in trading volume). The stochastic control framework, HJB equation solution, and optimal quoting strategy are directly applicable to algorithmic trading in prediction markets. The Monte Carlo comparison with a myopic benchmark demonstrates practical risk-reduction benefits. Highly relevant for quantitative traders operating in prediction market limit order books.

Requires solving a three-dimensional nonlinear PDE (reduced HJB equation) numerically using finite difference methods with implicit Euler, LU decomposition, and fixed-point iteration. The model involves a latent belief SDE, logistic transformation, Poisson order arrival processes, and inventory constraints. The mathematical framework is sophisticated (stochastic control, HJB theory, fixed-point arguments, Holder spaces). Practical implementation requires careful handling of boundary conditions, grid discretization, and convergence of the nonlinear iteration.

The paper provides complete mathematical derivations, explicit parameter specifications (Table 1), a detailed numerical scheme (Section 4.2), and Monte Carlo simulation methodology. All assumptions are clearly stated. However, no code or repository is provided, and the numerical implementation details (grid sizes, tolerances) are not fully specified.