Quantifying an Impact of Dimensional Change in Stochastic Portfolio Theory

In this paper, we develop the theory of functional generation of portfolios in an equity market of a 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 the most 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 relative portfolio performance with respect to the market