Related papers: Two parallel insurance lines with simultaneous arr…
In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance…
The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and…
We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities…
The occurrence of a claim often impacts not one but multiple insurance coverages provided in the contract. To account for this multivariate feature, we propose a new individual claims reserving model built around the activation of the…
Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to…
Due to the presence of reporting and settlement delay, claim data sets collected by non-life insurance companies are typically incomplete, facing right censored claim count and claim severity observations. Current practice in non-life…
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…
In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or…
We study the closure properties of the class of Bivariate Regular Variation, symbolically BRV , in standard and nonstandard cases, with respect to the randomly weighted sums. However, we take into consideration a weak dependence structure…
It has been decades since the academic world of ruin theory defined the insolvency of an insurance company as the time when its surplus falls below zero. This simplification, however, needs careful adaptions to imitate the real-world…
We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…
This paper introduces a unified micro-level stochastic framework for the joint modeling of loss reserves (RBNS), incurred but not reported (IBNR) reserves, and unearned premium risk under dependence, inflation, and discounting. The proposed…
The interest to retrial queueing systems is due to their application to telephone systems. The paper studies multiserver retrial queueing systems with $n$ servers. Arrival process is a quite general point process. An arriving customer…
The optimal stopping problem for the risk process with interests rates and when claims are covered immediately is considered. An insurance company receives premiums and pays out claims which have occured according to a renewal process and…
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…
This paper considers a particular renewal-reward process with multivariate discounted rewards (inputs) where the arrival epochs are adjusted by adding some random delays. Then this accumulated reward can be regarded as multivariate…
Retrial phenomenon naturally arises in various systems such as call centers, cellular networks and random access protocols in local area networks. This paper gives a comprehensive survey on theory and applications of retrial queues in these…
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…