Related papers: On the ruin problem in the renewal risk processes …
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation…
We reprove a result concerning certain ruin in the classical problem of the probability of ruin with risky investments and several of it's generalisations. We also provide the combined transition density of the risk and investment processes…
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…
Inspired by works of Landriault et al. \cite{LRZ-0, LRZ}, we study discounted penalties at ruin for surplus dynamics driven by a spectrally negative L\'evy process with Parisian implementation delays. To be specific, we study the so-called…
We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type…
In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…
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…
In this paper we investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also…
In this paper, we consider a classical risk model refracted at given level. We give an explicit expression for the joint density of the ruin time and the cumulative number of claims counted up to ruin time. The proof is based on solving…
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…
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…
In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$…
In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us…
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 study a ruin problem for an annuity model where a fixed fraction of capital is invested in a risky asset. Under weak assumptions on jumps, the ruin probability solves a second-order integro-differential equation and decays as a power…
We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. (2005) for such processes…
We study the probability of ruin before time $t$ for the family of tempered stable L\'evy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution…
In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance…
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…