From asymptotic properties of general point processes to the ranking of financial agents

Understand

We propose a general non-linear order book model that is built from the individual behaviours of the agents.

• Our framework encompasses Markovian and Hawkes based models.
• Under mild assumptions, we prove original results on the ergodicity and diffusivity of such system.
• Then we provide closed form formulas for various quantities of interest: stationary distribution of the best bid and ask quantities, spread, liquidity fluctuations and price volatility.