Extreme values of particular nonlinear processes

International audienceWe investigate the asymptotic behavior of the maxima of a general class of deterministic chaotic processes –including the Tent map and the Logistic map -, of noisy chaotic processes, and of the Gaussian long memory k-factor Genebauer processes

Extreme values of particular nonlinear processes

We investigate the asymptotic behavior of the maxima of a general class of deterministic chaotic processes –including the Tent map and the Logistic map -, of noisy chaotic processes, and of the Gaussian long memory k-factor Genebauer processes.Chaotic system – Extreme value theory – long memory processes – GIGARCH.

Une mesure de la persistance dans les indices boursiers.

We identify and examine the presence of the long memory in equity returns and more generally in specific transformations of these returns, on both the US and European stock markets. Taking into account the persistence phenomenon, we analyze the effect of the splitting of the sample period on the one hand, and the impact of the aggregation on the other hand, on the long me-mory process. Our main results show the strongest evidence of long memory presence in the absolute value of the returns.Long memory; Persistence phenomenon; Stock markets.

Asymptotic results for conditional measures of association of a random sum

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the "one-jump"property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate the tail index of the underlying distribution