Quantifying dimensional change in stochastic portfolio theory
研究了股票市场因上市或退市导致维度变化时，如何构建自融资投资组合，并量化维度变化对投资组合收益的影响，附有实证分析。
Abstract In this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self‐financing stock portfolios (additive, multiplicative, and rank‐based) in a very general setting. Our study explains how a dimensional change caused by a listing or delisting event of a stock, and unexpected shocks in the market, affect portfolio return. We also provide empirical analyses of some classical portfolios, quantifying the impact of dimensional change in portfolio performance relative to the market.