预测市场中的最优做市
Optimal Market Making in Prediction Markets
浏览论文内容
中文总结 AI 辅助
研究预测市场中的最优做市问题，开发随机控制框架，将市场价格建模为条件概率，推导方程并刻画最优报价，经变换证明解的存在唯一性，通过数值分析揭示其依赖因素，还表明该策略能改善下行保护并保留预期利润。
中文摘要 AI 辅助
随着交易量上升和实际相关性增加，预测市场正吸引越来越多关注。为确保有效价格发现，流动性供应愈发重要。由于预测市场的二元结算结构，最优做市导致一个与经典环境中研究的问题根本不同的优化问题。本文为预测市场开发了一个随机控制框架，其中市场价格被建模为通过变换后的潜在信念扩散产生的结果的条件概率。做市商选择买卖报价以最大化预期终端财富，同时控制市价库存风险和结算时剩余头寸的结算风险。我们推导了相关的汉密尔顿 - 雅可比 - 贝尔曼方程，并刻画了唯一的最优买卖报价。通过将方程变换到潜在信念空间并使用不动点论证，我们证明了经典解的存在性和唯一性，并验证了所得的最优报价策略。此外，我们提供了数值分析，揭示了预测市场中的最优流动性供应如何依赖于库存、市场信念、结算时间和风险厌恶。进一步，我们表明相对于最大化即时预期市价利润的近视基准，最优报价策略在保留大部分预期利润的同时显著改善了下行保护。
英文摘要
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.
