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We formulate the insurance risk process in a general Levy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to…

Probability · Mathematics 2007-05-23 Claudia Kluppelberg , Andreas E. Kyprianou , Ross A. Maller

Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a L\'evy insurance risk process under the Cram\'er-Lundberg and convolution equivalent conditions. For example, the limiting distributions…

Probability · Mathematics 2016-01-08 Philip S. Griffin

We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion…

Risk Management · Quantitative Finance 2010-11-08 Serguei Pergamenchtchikov , Zeitouny Omar

We study the rough asymptotic behaviour of a general economic risk model in a discrete setting. Both financial and insurance risks are taken into account. Loss during the first $n$ years is modelled as a random variable…

Probability · Mathematics 2015-11-25 Jaakko Lehtomaa

Important models in insurance, for example the Carm{\'e}r--Lundberg theory and the Sparre Andersen model, essentially rely on the Poisson process. The process is used to model arrival times of insurance claims. This paper extends the…

Statistics Theory · Mathematics 2019-04-16 Arun Kumar , Nikolai Leonenko , Alois Pichler

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 consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cram\'er-Lundberg model, namely the constant jump intensity of the Poisson process. Due to this…

Probability · Mathematics 2022-05-11 Simon Pojer , Stefan Thonhauser

Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial…

Probability · Mathematics 2020-04-28 Lanpeng Ji

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…

Risk Management · Quantitative Finance 2021-12-14 Helena Jasiulewicz , Wojciech Kordecki

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…

Risk Management · Quantitative Finance 2017-10-31 Wenhao Li , Bolong Wang , Tianxiang Shen , Ronghua Zhu , Dehui Wang

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…

Probability · Mathematics 2024-01-22 Grigori Jasnovidov , Aleksandr Shemendyuk

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…

Probability · Mathematics 2020-02-04 Anita Behme , Claudia Klüppelberg , Gesine Reinert

This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlying process, our model allows each process to operate…

Probability · Mathematics 2023-08-01 Hamed Amini , Andreea Minca , Oscar Peralta

We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function $P(u)$ for the component-wise ruin (that is both…

Probability · Mathematics 2019-08-07 Krzysztof Debicki , Lanpeng Ji , Tomasz Rolski

In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We focus on general spectrally negative L\'{e}vy insurance risk process. For this…

Probability · Mathematics 2010-04-21 Irmina Czarna , Zbigniew Palmowski

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…

Probability · Mathematics 2018-12-24 G. A. Delsing , M. R. H. Mandjes , P. J. C. Spreij , E. M. M. Winands

The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite-time horizon. This is not the case for the simultaneous ruin probability in two-dimensional Brownian risk model. Resorting…

Probability · Mathematics 2018-11-13 Krzysztof Dȩbicki , Enkelejd Hashorva , Zbigniew Michna

We derive exact tail asymptotics of the Parisian ruin probability for Gaussian risk models driven by locally self-similar Gaussian processes with a power-type deterministic trend. The considered setting includes non-stationary Gaussian…

Probability · Mathematics 2026-04-02 Svyatoslav M. Novikov

In a dual risk model, the premiums are considered as the costs and the claims are regarded as the profits. The surplus can be interpreted as the wealth of a venture capital, whose profits depend on research and development. In most of the…

Risk Management · Quantitative Finance 2024-12-02 Lingjiong Zhu

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