This paper shows the infinite time ruin probability for an insurance company in the classical Cramér-Lundberg model with finite exponential moments.

We consider a risk process modelled as a compound Poisson process. We find the otimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a...

We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton- Jacobi- Bellmann equation as well...

The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform.

For the Cramer-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in...

We study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution...

In this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. ... We use an inversion formula based on the real part only, to get the original function.

We are dealing with the ruin probability and the expected ruin time in a two state Markov model ...

A method of inverting the Laplace transform based on the integration between zeros technique and a simple acceleration algorithm is presented. This approach was designed to approximate ultimate ruin probabilities for G-convolutions claim sizes, but it can be also used with other distributions...

The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require...