初始资本下的交易先知问题 (Trading Prophets with Initial Capital)

Correa et al. [EC' 2023] introduced the following trading prophets problem. A trader observes a sequence of stochastic prices for a stock, each drawn from a known distribution, and at each time must decide whether to buy or sell. Unfortunately, they observed that in this setting it is impossible to compete with a prophet who knows all future stock prices. In this paper, we explore the trading prophets problem when we are given initial capital with which to start trading. We show that initial capital is enough to bypass the impossibility result and obtain a competitive ratio of $3$ with respect to a prophet who knows all future prices (and who also starts with capital), and we show that this competitive ratio is best possible. We further study a more realistic model in which the trader must pay multiplicative and/or additive transaction costs for trading which model dynamics such as bid-ask spreads and broker fees.

翻译：Correa 等人 [EC' 2023] 提出了以下交易先知问题。交易者观察股票的一系列随机价格，每个价格均从已知分布中抽取，且必须在每个时刻决定买入或卖出。然而他们发现，在此设定下，无法与知晓所有未来股价的先知进行竞争。本文探讨了在给定初始资本以启动交易情况下的交易先知问题。我们证明，初始资本足以规避该不可能性结果，并能获得相对于知晓所有未来价格（且同样拥有初始资本）的先知的竞争比为 $3$，同时我们证明该竞争比是最优的。我们进一步研究了一个更现实的模型，其中交易者进行交易时需支付乘性和/或加性交易成本，此类成本可用于模拟买卖价差和经纪佣金等动态因素。