  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.
