论文标题
$ n $投资者之间的互动相对套利机会
Relative Arbitrage Opportunities with Interactions among $N$ Investors
论文作者
论文摘要
相对套利投资组合的表现优于给定时间概率的基准投资组合。随着风险过程的市场价格，根据市场组合和投资者的不同，本文分析了市场和财富动态系统中相对套利机会的多代理优化。我们在经验衡量投资者的经验衡量标准下构建了一个庞大的市场动态系统，每个投资者都寻求相对套利的基准依赖于市场和所有代理商。我们展示了通过Fichera Drift保证竞争投资者之间相对套利机会的条件。在温和的条件下，我们为投资者提供了最佳策略，以及取决于库奇问题最小的非负解决方案的独特NASH均衡。
The relative arbitrage portfolio outperforms a benchmark portfolio over a given time-horizon with probability one. With market price of risk processes depending on the market portfolio and investors, this paper analyzes the multi-agent optimization of relative arbitrage opportunities in the coupled system of market and wealth dynamics. We construct a well-posed market dynamical system of McKean-Vlasov type under an empirical measure of investors, where each investor seeks for relative arbitrage with respect to a benchmark dependent on market and all the agents. We show the conditions to guarantee relative arbitrage opportunities among competitive investors through the Fichera drift. Under mild conditions, we derive the optimal strategies for investors and the unique Nash equilibrium that depends on the smallest nonnegative solution of a Cauchy problem.
