Jonas Šiaulys

On the ruin probability in a dependent discrete time risk model with insurance and financial risks

This paper considers the discrete-time risk model with insurance risk and financial risk in some dependence structures. Under assumptions that the insurance risks are heavy tailed (belong to the intersection of the long-tailed class and the dominatedly varying-tailed class) and the financial risks satisfy some moment conditions, the asymptotic and uniformly asymptotic relations for the finite-time and ultimate ruin probabilities are derived.

Factorial Moments of Distributions of Additive Functions

AbstractWe study the weak convergence of the distribution functions

\mathcal{O}

[x]^{ - 1} \# \{ m \leqslant x:f_x (m) < u\} .

Bi-seasonal discrete time risk model

Here fx is a set (x ⩾ 2) of integer-valued strongly additive functions. The method of factorial moments is crucial in the proofs.

Gerber–Shiu function for the discrete inhomogeneous claim case

Let

Precise large deviations for compound random sums in the presence of dependence structures

\{\xi_1,\xi_2,\ldots\}

Randomly stopped maximum and maximum of sums with consistently varying distributions

be a sequence of independent random variables (not necessarily identically distributed), and

A Lundberg-type inequality for an inhomogeneous renewal risk model

\eta