In response to criticism concerning the current solvency system, the European Commission is developing new rules for insurance companies operating in the member states of the European Union (EU). Under this so-called Solvency II concept, an insurer is allowed to verify its solvency by using an internal risk management model previously approved by the regulatory authority. In this article we dev...

We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior t...

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...

Assume that a compound Poisson surplus process is invested in a stochastic interest process which is assumed to be a Lévy process. We derive recursive and integral equations for ruin probabilities with such an investment. Lower and upper bounds for the ultimate ruin probability are obtained from these equations. When the interest process is a Brownian motion with drift, we give a unified treatm...

For general risk processes, we introduce and study the expected time-integrated negative part of the process on a fixed time interval. Differentiation theorems are stated and proved. They make it possible to derive the expected value of this risk measure, and to link it with the average total time below 0, studied by Dos Reis, and the probability of ruin. We carry out differentiation of other f...

in this paper, a compound binomial risk model in the presence of a constant dividend barrier is studied. two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. in the evaluation of the moments of the present value of dividends, the interest rates are ass...

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...