Related papers: Number of claims and ruin time for a refracted ris…
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.
In this paper we propose new iterative algorithm of calculating the joint distribution of the Parisian ruin time and the number of claims until Parisian ruin for the classical risk model. Examples are provided when the generic claim size is…
The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.
This paper deals with the discrete-time risk model with nonidentically distributed claims. We suppose that the claims repeat with time periods of three units, that is, claim distributions coincide at times $\{1,4,7,\ldots\}$, at times…
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 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…
We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an…
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…
We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our…
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 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 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 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…
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…
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…
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…
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…
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…
We study a multidimensional renewal risk model, with common counting process and cadlag returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly…
Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes…