Related papers: Fractional Risk Process in Insurance
We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the…
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 paper, we introduce a risk process, namely, the mixed fractional risk process (MFRP) in which the number of claims in the associated claim process are modelled using the mixed fractional Poisson process (MFPP). The covariance…
This paper studies the properties of the Multiply Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs…
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…
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…
We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events,…
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…
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…
Contemporary insurance theory is concentrated on models with different types of polices and shock events may influence the payments on some of them. Jordanova (2018) considered a model where a shock event contributes to the total claim…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to…
This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted)…
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…
It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, without and with reward, respectively. We first recall the…
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 consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ($i=1,2,\dots$) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model…
Modelling wildfire events has been studied in the literature using the Poisson process, which essentially assumes the independence of wildfire events. In this paper, we use the fractional Poisson process to model the wildfire occurrences 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…
In light of intense hurricane activity along the U.S. Atlantic coast, attention has turned to understanding both the economic impact and behaviour of these storms. The compound Poisson-lognormal process has been proposed as a model for…