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 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 a virtual organization directed on the insurance business, the estimations of the risk process and of the ruin probability are important concerns: for researchers, at the theoretical level, and for the management of the company, as these influence the insurer strategy. We consider the...

A user friendly approach to modeling the risk process is presented. It utilizes the insurance library of the XploRe computing environment which is accompanied by on-line, hyperlinked and freely downloadable from the web manuals and e-books. The empirical analysis for Danish fire losses for the...

We find an exact asymptotics of the ruin probability $\Psi (u)$ when the capital of insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility $\sigma0$. In contrast to the classical case of non-risky investments where the...

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...

In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

This chapter develops on risk processes which, perhaps, are most suitable for computer visualization of all insurance objects. At the same time, risk processes are basic instruments for any non-life actuary – they are vital for calculating the amount of loss that an insurance company may incur.