Fractional Poisson process: long-range dependence and applications in ruin theory

The fractional Poisson field (fPf) can be interpreted in term of the number of balls falling down on each point of R D , when the centers and the radii of the balls are thrown at

Renewal process, fractional Poisson process and distribution, fractional Kolmogorov-Feller equation, continuous time random walk, generalized fractional diffusion.. ∗

This section is dedicated to numerical illustrations of the theoretical results regarding some exact and asymptotic expressions of the mean, variance, covariance and correlation of

Keywords Ruin probabilities · Dual models · Price process · Renewal theory · Distribu- tional equation · Autoregression with random coefficients · L´evy process.. Mathematics

Asymptotic multivariate finite-time ruin probabilities with heavy- tailed claim amounts: Impact of dependence and optimal reserve allo- cation.. ROMAIN

The fractional Poisson field (fPf) is constructed by considering the number of balls falling down on each point of R D , when the centers and the radii of the balls are thrown at

Keywords: compound Poisson model, ultimate ruin probability, natural exponential fam- ilies with quadratic variance functions, orthogonal polynomials, gamma series expansion,

The mean of the absolute values of the forecasting errors obtained with this estimator is approximately equal to 771 ft 3 /s, and the forecast of the flow on the next day is better,