This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating...

This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating...

This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating...

Let be i.i.d. -valued random variables. We prove partial moderate deviation principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.

For {Xi}i = 1 a sequence of i.i.d. random variables taking values in a Polish space [Sigma] with distribution [mu], we obtain large and moderate deviation principles for the processes {n-1 [Sigma][nt]i = 1 [delta]Xi; t = 0}n = 1 and {n-1/2 [Sigma][nt]i = 1 ([delta]Xi - [mu]); t = 0}n = 1,...

Consider a sequence of m deterministic points in ##R##d, and consider the empirical measure of a random sample (without replacements) of size n = n(m). We prove the large deviation principle and compute the resulting rate function for the latter empirical measure under the assumptions that the...