Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2849-2883 |
| Number of pages | 35 |
| Journal | Annals of Applied Probability |
| Volume | 29 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2019 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- Capital distribution
- Functionally generated portfolios
- Gaussian fluctuations
- Hitting times
- Hydrodynamic limits
- Macroscopic market observables
- Market diversity
- Market entropy
- Porous medium equation
- Rank-based models
- Relative return
- Stochastic partial differential equations
- Stochastic portfolio theory