Related papers: A transient Cram\'er-Lundberg model with applicati…
We study the asymptotics of the ruin probability in the Cram\'er-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive…
The classical Cram\'er-Lundberg risk process models the ruin probability of an insurance company experiencing an incoming cash flow - the premium income, and an outgoing cash flow - the claims. From a system's viewpoint, the web of…
This paper considers a Cram\'er-Lundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claim-size distribution, and the premium rate, but we…
In this paper, we discuss the Cram\'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift $a$ and volatility $\sigma> 0.$ By assuming there is a cap on the claim sizes,…
This paper considers the Cram\'er-Lundberg model, with the additional feature that the number of clients can fluctuate over time. Clients arrive according to a Poisson process, where the times they spend in the system form a sequence of…
The classical Cramer-Lundberg model was the first attempt to describe the financial condition of the insurance company. The incomes were approximated by a steady stream of money, insurance payments were not limited and could take any value…
We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events,…
We consider a bivariate Cramer-Lundberg-type risk reserve process with the special feature that each insurance company agrees to cover the deficit of the other. It is assumed that the capital transfers between the companies are…
We study the asymptotic behavior of ruin probabilities, as the initial reserve goes to infinity, for a reserve process model where claims arrive according to a renewal process, while between the claim times the process has the dynamics of…
We analyze the probability of ruin for the {\it scaled} classical Cram\'er-Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart \cite{I1969} to the actuarial literature, amounts to…
We investigate the Levy insurance risk model with tax under Cram\'er's condition. A direct analogue of Cram\'er's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin…
The Cram\'er-Lundberg model with exponential claims and proportional investment is solved exactly: the integro-differential equation for the survival probability reduces to a doubly confluent Heun equation, yielding an explicit solution in…
Let $\{B(t), t\ge 0\}$ be a Brownian motion. Consider the Brownian motion risk model with interest rate collection and tax payment defined by \begin{align}\label{Rudef}…
In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit condition causes guaranteed ruin in few but simple cases…
We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion.…
We consider an approach to credit risk in which the information about the time of bankruptcy is modelled using a Brownian bridge that starts at zero and is conditioned to equal zero when the default occurs. This raises the question whether…
Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a L\'evy insurance risk process under the Cram\'er-Lundberg and convolution equivalent conditions. For example, the limiting distributions…
We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…
We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the…
In this work the ruin probability of the Lundberg risk process is used as a criterion for determining the optimal security loading of premia in the presence of price-sensitive demand for insurance. Both single and aggregated claim processes…