189 citations · 697 across the 47 of their papers we have counts for
13 papers · 1 filter
An expansion formula for Hawkes processes and application to cyber-insurance derivatives
Caroline Hillairet, Anthony Reveillac, Mathieu Rosenbaum
In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the well-known…
Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint
Eyal Neuman, Mathieu Rosenbaum
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial a…
Asymptotic behavior of local times related statistics for fractional Brownian motion
Mark Podolskij, Mathieu Rosenbaum
We consider high frequency observations from a fractional Brownian motion. Inspired by the work of Jean Jacod in a diffusion setting, we investigate the asymptotic behavior of vari…
Asymptotic Optimal Tracking: Feedback Strategies
Jiatu Cai, Mathieu Rosenbaum, Peter Tankov
This is a companion paper to (Cai, Rosenbaum and Tankov, Asymptotic lower bounds for optimal tracking: a linear programming approach, arXiv:1510.04295). We consider a class of stra…
Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach
Jiatu Cai, Mathieu Rosenbaum, Peter Tankov
We consider the problem of tracking a target whose dynamics is modeled by a continuous Itō semi-martingale. The aim is to minimize both deviation from the target and tracking effor…
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes
Thibault Jaisson, Mathieu Rosenbaum
We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has norm close to one and power law tail of the form ,…