Marc Hoffmann

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We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative(More)
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] in the limit T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme with(More)
In the context of statistics for random processes, we prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] when T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the(More)
Multifractal analysis of multiplicative random cascades is revisited within the framework of mixed asymptotics. In this new framework, statistics are estimated over a sample which size increases as the resolution scale (or the sampling period) becomes finer. This allows one to continuously interpolate between the situation where one studies a single cascade(More)
We study the problem of estimating the coefficients of a diffusion (Xt , t ≥ 0); the estimation is based on discrete data Xn ,n = 0,1, . . . ,N . The sampling frequency −1 is constant, and asymptotics are taken as the number N of observations tends to infinity. We prove that the problem of estimating both the diffusion coefficient (the volatility) and the(More)
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the(More)
There exist several algorithm setups to realize object recognition systems. But actually it is a challenging task to implement these technologies for real-time applications in embedded, mobile devices. One reason for that is that the required processing power for real-time algorithms, which are required to offer a reliable system, is not available. One(More)
Hawkes processes are used for modeling tick-by-tick variations of a single or of a pair of asset prices. For each asset, two counting processes (with stochastic intensities) are associated respectively with the positive and negative jumps of the price. We show that, by coupling these two intensities, one can reproduce high-frequency mean reversion structure(More)