  First introduced by Fernholz in stochastic portfolio theory, functionally
generated portfolio allows its investment performance to be attributed to
directly observable and easily interpretable market quantities. In previous
works we showed that Fernholz's multiplicatively generated portfolio has deep
connections with optimal transport and the information geometry of
exponentially concave functions. Recently, Karatzas and Ruf introduced a new
additive portfolio generation whose relation with optimal transport was studied
by Vervuurt. We show that additively generated portfolio can be interpreted in
terms of the well-known dually flat information geometry of Bregman divergence.
Moreover, we characterize, in a sense to be made precise, all possible forms of
functional portfolio constructions that contain additive and multiplicative
generations as special cases. Each construction involves a divergence
functional on the unit simplex measuring the market volatility captured, and
admits a pathwise decomposition for the portfolio value. We illustrate with an
empirical example.
