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Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage

The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path stochastic portfolio theory of E. R. Fernholz. FGPs have been formulated to yield a master equation---a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the numeraire. This description has proved to be analytically very useful, as it is both pathwise and free of stochastic integrals. In this paper we generalize the class of FGPs in two ways: (1) the numeraire may be any strictly positive wealth process, not necessarily the market portfolio or even a passive portfolio; and (2) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation. These generalizations do not forfeit the important tractability properties of the associated master equation. We show how these generalizations can be usefully applied to statistical arbitrage, portfolio risk immun...