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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…
In this paper, we investigate Parisian ruin for a L\'evy surplus process with an adaptive premium rate, namely a refracted L\'evy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also…
In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin…
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…
The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric L\'evy process. Considering the ruin probability as a of the capital reserve we obtain for…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
We introduce the hybrid risk process, constructed via a time-change transformation applied to the solution of a hybrid stochastic differential equation. The framework covers several modern ruin settings, incorporating features like…
This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability…
This paper studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is…
We investigate the asymptotic of ruin probabilities when the company invests its reserve in a risky asset with a switching regime price. We assume that the asset price is a conditional geometric Brownian motion with parameters modulated by…
In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
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…
This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the…
In this text, we establish the risk model based on AR(1) series and propose the basic model which has a dependent structure under intensity of claim number. Considering some properties of the risk model, we take advantage of newton…
The ability to estimate the rate of convergence for the distributions of regenerative processes is in great demand. These processes are often encountered in queuing theory and in related problems. In some papers on regenerative processes,…
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 paper, we generalise the results presented in the literature for the ruin probability for the insurer--reinsurer model under a pro-rata reinsurance contract. We consider claim amounts that are described by a phase-type distribution…
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.
In this paper we determine bounds and exact asymptotics of the ruin probability for risk process with arrivals given by a linear marked Hawkes process. We consider the light-tailed and heavy-tailed case of the claim sizes. Main technique is…