A. Almada Monter Sergio et al., Dynamics of observables in rank-based models and performance of functionally generated portfolios, Annals of applied probability , 29(5), 2019, pp. 2849-2883
In the seminal work (Stochastic Portfolio Theory: Stochastic Modelling and Applied Probability (2002) Springer), several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. We fill this gap in the setting of rank-based models. The results are then used to study the performance of multiplicatively and additively functionally generated portfolios.