The Pareto Copula, Aggregation of Risks and the Emperor's Socks

The Pareto Copula, Aggregation of Risks and the Emperor's Sock

SOME LIMIT THEORY FOR THE SELF-NORMALIZED PERIODOGRAM OF STABLE PROCESSES

Let X(t) = Sigma(j)(infinity) = (-infinity) psi(j)Z(t-j) be a discrete moving average process based on i.i.d. random variables (Z(t),)(t epsilon Z) with common distribution function from the domain of normal attraction of a p-stable law (0 <p less than or equal to 2). We prove weak convergence of the self-normalised periodogram [GRAPJICS] Furthermore, we show that smoothed versions of ($) over bar I-n,(X)(lambda) provide consistent estimates for the normalised transfer function for any p epsilon (0, 2] independent of p

Large deviations of heavy-tailed random sums with applications in insurance and finance

We prove large deviation results for the random sum S(t)=Sigma(i=1)(N(t)) X-i, t greater than or equal to 0, where (N(t))(t greater than or equal to 0) are non-negative integer-valued random variables and (X-n)(n is an element of N) are i.i.d. non-negative random Variables with common distribution function F, independent of (N(t))(t greater than or equal to 0). Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims

Densities with Gaussian tails

Densities with Gaussian tail

Tauberian results for densities with Gaussian tails

ISSN:0024-6107ISSN:1469-775