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In the seminal work [9], 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 and expect our ideas to extend to other models of large financial markets as well. The results are then used to study the performance of multiplicatively and additively functionally generated portfolios, in particular, over short-term and medium-term horizons.
We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward perfo
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obt
We consider systems of diffusion processes (particles) interacting through their ranks (also referred to as rank-based models in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations
In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study
The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote It remains to investigate whether, and in what sense, the nonlinear determin-istic model formulation is the limit of