文献类型：期刊文献

英文题名：Quantum Probability Theoretic Asset Return Modeling: A Novel Schr?dinger-Like Trading Equation and Multimodal Distribution

作者：Li, Lin[1,2]

机构：[1] Department of Finance, Business School, East China University of Science and Technology, Shanghai, 200237, China; [2] Risk-Center, ETH Zürich, CH8092, Switzerland

年份：2024

外文期刊名：arXiv

收录：EI(收录号：20240036955)

语种：英文

外文关键词：Commerce - Financial markets - Stochastic systems - Wave functions

摘要：Quantum theory offers a comprehensive framework for quantifying uncertainty, and many studies in quantum finance explore the stochastic nature of asset returns based on this theory, where the returns are likened to the motion of microscopic particles, adhering to physical laws characterized by quantum probabilities. However, such approaches inevitably presuppose that the changes in returns exhibit certain microscopic quantum effects, a presumption that may not guaranteed and has been criticized. In contrast to conventional approaches, this paper takes a novel perspective by asserting that quantum probability is primarily a mathematical scheme extending the classical probability from real to complex numbers, not exclusively tied to microscopic quantum phenomena. By directly linking the mathematical structure of quantum probability to traders’ decisions and market trading behaviors, it circumvents the presupposition of quantum effects for returns and invocation the wave function. The phase in complex form of quantum probability serves as a additional element, capturing transitions between long and short decisions but also take information interaction among traders into account, This gives quantum probability an inherent advantage over classical probability in characterizing the multimodal distribution of asset returns. Through Fourier decomposition, we derive a Schr?dinger-like trading equation, wherein each term corresponds explicitly to implications of market trading. The equation suggests discrete energy levels in financial trading, and returns follows the normal distribution at the lowest level. As the market shifts to higher trading levels, a phase transition occurs in the distribution of returns, leading to multimodality and fat tails. Empirical research on the Chinese stock market supports the existence of energy levels and multimodal distributions from this quantum probability asset returns model. ? 2024, CC BY.