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...

In this paper, we study a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The...

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 a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the finite time ruin probability is well given when the claim amount distribution is a mixed exponential... br>