Related papers: Risk theory in a finite customer-pool setting
Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of…
Using the results of precise large deviation and renewal theory for widely dependent random variables, this paper obtains the asymptotic estimation of the random-time ruin probability and the uniform asymptotic estimation of finite-time…
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 article, we introduce a new definition of bankruptcy for a spectrally negative L\'evy insurance risk process. More precisely, we study the Gerber-Shiu distribution for a ruin model where at each time the surplus goes negative, an…
We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the…
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…
In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [1] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In…
In this note we consider the two-dimensional risk model introduced in Avram et al. \cite{APP08} with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite…
In this paper, we build on the techniques developed in Albrecher et al. (2013), to generate initial-boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim…
This paper investigates ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. We focus on joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of…
The basic principle of any version of insurance is the paradigm that exchanging risk by sharing it in a pool is beneficial for the participants. In case of independent risks with a finite mean this is the case for risk averse decision…
We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…
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…
We consider the multivariate risk model with common renewal process among the lines of business, and Brownian perturbations. Assuming that the integrated tail distribution of claims is multivariate subexponential, we establish an asymptotic…
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…
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve…
In this note, we study the ultimate ruin probabilities of a real-valued L{\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\'e}vy processes, the probability of ruin decreases as an exponential function…
The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a L\'evy process. Assuming a parametric family for the L\'evy measures, we estimate the parameter from the…
We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin…
In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time $T$ follows a normal distribution with a given mean and a given variance. In both…