In this paper, we show that the delayed Sparre Andersen insurance risk model in discrete time can be analyzed as a doubly infinite, right skip-free Markov chain. We then describe how matrix analytic methods can be used to establish a computational procedure for calculating the probability distributions associated with fundamental ruin-related quantities of interest, such as the time of ruin, th...

We describe an approach to the evaluation of the moments of the time of ruin in the classical Poisson risk model. The methodology employed involves the expression of these moments in terms of linear combinations of convolutions involving compound negative binomial distributions. We then adapt the results for use in the practically important case involving phase-type claim size distributions. We...

In this paper we extend the classical Cramér-Lundberg risk model by including tax payments. The considered tax rule is to pay a certain proportion of the premium income, whenever the portfolio is in a profitable situation. It is shown that the resulting survival probability is a power of the survival probability without tax. Furthermore, an explicit expression for the expected discounted total ...

We consider finite time ruin problems in the Markov-modulated risk model. We start by considering the number of claims and the aggregate claim amount over a finite time interval, in each case giving both a general approach for an arbitrary number of environment states and a specific approach for the special case when the number of environment states is two. We then consider the density of the t...

In this paper, the author aim to present a threat and risk-driven methodology to security requirements engineering. The chosen approach has a strong focus on gathering, modeling, and analyzing the environment in which a secure ICT-system to be built is located. The knowledge about the environment comprises threat and risk models. As presented in the paper, this security-relevant knowledge is us...

Periodicity and Ruin Probabilities for Compound Non-Homogenous Poisson Processes Compound non-homogenous Poisson processes with periodic claim intensity rates are stiidied in this work. A risk process related to a short term periodic environment and the periodicity for its compound claim counting process are discussed. The ruin probabilities of compo~md non-homogenous Poisson processes with per...

We study a discrete-time interaction risk model with delayed claims within the framework of the compound binomial model. Using the technique of generating functions, we derive both a recursive formula and a defective renewal equation for the expected discounted penalty function. As applications, the probabilities of ruin and the joint distributions of the surplus one period to ruin and the defi...

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed by Trefethen et al. [12]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show ...

The use of internal Bank models for meeting capital requirements has been approved for some time. Regulators then face issues of model approval necessitating some public domain analysis of model performance. This paper presents a new approach to risk model evaluation using forward looking risk neutral probabilities. In addition to V aR and CV aR we analyse a new measure termed here RWAV aR that...