Related papers: Ruin Probabilities for Risk Processes in Stochasti…
We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative…
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…
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…
This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram\'er-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost…
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 apply the theory of linear recurrence sequences to find an expression for the ultimate ruin probability in a discrete-time risk process. We assume the claims follow an arbitrary distribution with support $\{0,1,\ldots,m\}$, for some…
Consider a surplus process which both of collected premium and payed claim size are two independent compound Poisson processes. This article derives two approximated formulas for the ruin probability of such surplus process, say double…
The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than…
We consider a spectrally-negative Markov additive process as a model of a risk process in random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees…
We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
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.…
This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently…
We develop a model for contagion in reinsurance networks by which primary insurers' losses are spread through the network. Our model handles general reinsurance contracts, such as typical excess of loss contracts. We show that simpler…
We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets…
This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlying process, our model allows each process to operate…
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…
Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak…
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 risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin…