We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events, this process is time-changed by a Lévy subordinator....

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the main problems is to decide if there is any type of...

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the main problems is to decide if there is any type of...

We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival times depending on the claims that arrive within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the bonus-malus...

We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival times depending on the claims that arrive within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the bonus-malus...

Let L and S denote the classes of distributions with long tails and subexponential tails respectively. Let OS denote the class of distributions with O-subexponential tails, which means the distributions with the tails having the same order as the tails of their 2-fold convolutions. In this...

A risk process with constant premium rate $c$ and Poisson arrivals of claims is considered. A threshold $r$ is defined for claim interarrival times, such that if $k$ consecutive interarrival times are larger than $r$, then the next claim has distribution $G$. Otherwise, the claim size...