In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax independence and stationarity assumptions and extend some asymptotic...

In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments. We compare the two approximations studying mixture of exponentials and lognormal...

A finite horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Obtaining explicit optimal solutions for the minimizing ruin probability problem is a difficult task. Therefore, we consider an alternative method...

This paper is intended as a guide to simulation of risk processes. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the...

This paper is devoted to discrete processes of dependent risks. The random variables describing the time between claims can be dependent in such processes, unlike under the classical approach. The ruin problem is investigated and the probability of ruin is computed. The relation between the...

In this paper we study an optimal investment problem of an insurer when the company has the opportunity to invest in a risky asset using stochastic control techniques. A closed form solution is given when the risk preferences are exponential as well as an estimate of the ruin probability when...

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. Working with a classical surplus process with exponential jump size, we...

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. We obtain the probability of ruin in the infinite horizon for the case when...