2017/09/10 by Ting‐Kam Leonard Wong, Wong, Ting-Kam Leonard
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Risk and Portfolio Optimization #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1709.03169
openalex publication_date 2017/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.