相关论文: Extreme times in financial markets
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
An intense research on financial market microstructure is presently in progress. Continuous time random walks (CTRWs) are general models capable to capture the small-scale properties that high frequency data series show. The use of CTRW…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). The extremes studied are the maximum, the…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time…
For a zero-delayed random walk on the real line, let $\tau(x)$, $N(x)$ and $\rho(x)$ denote the first passage time into the interval $(x,\infty)$, the number of visits to the interval $(-\infty,x]$ and the last exit time from $(-\infty,x]$,…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
We consider open quantum walks on a graph, and consider the random variables defined as the passage time and number of visits to a given point of the graph. We study in particular the probability that the passage time is finite, the…
We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.