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Related papers: Risk theory in a finite customer-pool setting

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Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of…

Probability · Mathematics 2014-02-26 Hansjoerg Albrecher , Christian Robert , Jef Teugels

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…

Probability · Mathematics 2025-06-24 Yang Chen , Zhaolei Cui , Yuebao Wang

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…

Probability · Mathematics 2019-06-10 Corina Constantinescu , Guusje Delsing , Michel Mandjes , Leonardo Rojas Nandayapa

In this article, we introduce a new definition of bankruptcy for a spectrally negative L\'evy insurance risk process. More precisely, we study the Gerber-Shiu distribution for a ruin model where at each time the surplus goes negative, an…

Probability · Mathematics 2015-07-28 Juan Carlos Pardo , Jose Luis Perez , Victor Rivero

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…

Probability · Mathematics 2023-07-28 Oscar Peralta , Matthieu Simon

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…

Probability · Mathematics 2016-04-22 Corina Constantinescu , Suhang Dai , Weihong Ni , Zbigniew Palmowski

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…

Probability · Mathematics 2011-12-13 Søren Asmussen , Dominik Kortschak

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…

Probability · Mathematics 2012-07-17 Ze-Chun Hu , Bin Jiang

In this paper, we build on the techniques developed in Albrecher et al. (2013), to generate initial-boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim…

Probability · Mathematics 2021-01-12 Corina Constantinescu , Zbigniew Palmowski , Jing Wang

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…

Probability · Mathematics 2020-10-02 Krzysztof Kȩpczyński

The basic principle of any version of insurance is the paradigm that exchanging risk by sharing it in a pool is beneficial for the participants. In case of independent risks with a finite mean this is the case for risk averse decision…

Risk Management · Quantitative Finance 2025-10-08 Alfred Müller

We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…

Probability · Mathematics 2015-05-19 Yuri Kabanov , Serguei Pergamenshchikov

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…

Probability · Mathematics 2023-05-25 Peter Braunsteins , Michel Mandjes

We consider the multivariate risk model with common renewal process among the lines of business, and Brownian perturbations. Assuming that the integrated tail distribution of claims is multivariate subexponential, we establish an asymptotic…

Probability · Mathematics 2026-02-24 Dimitrios G. Konstantinides

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…

Probability · Mathematics 2026-04-01 Michel Denuit , José Miguel Flores-Contró , Christian Y. Robert

In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve…

Risk Management · Quantitative Finance 2008-12-02 Henrik Hult , Filip Lindskog

In this note, we study the ultimate ruin probabilities of a real-valued L{\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\'e}vy processes, the probability of ruin decreases as an exponential function…

Probability · Mathematics 2018-02-26 Jérôme Spielmann

The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a L\'evy process. Assuming a parametric family for the L\'evy measures, we estimate the parameter from the…

Probability · Mathematics 2021-12-15 Yasutaka Shimizu

We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin…

Probability · Mathematics 2019-05-15 Hansjörg Albrecher , Bohan Chen , Eleni Vatamidou , Bert Zwart

In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time $T$ follows a normal distribution with a given mean and a given variance. In both…

Mathematical Finance · Quantitative Finance 2022-06-13 Katia Colaneri , Julia Eisenberg , Benedetta Salterini