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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 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

We investigate the Levy insurance risk model with tax under Cram\'er's condition. A direct analogue of Cram\'er's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin…

Probability · Mathematics 2018-06-19 Philip Griffin

In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin.…

Optimization and Control · Mathematics 2011-12-20 Shangzhen Luo , Michael Taksar

We consider a risk model where deficits after ruin are covered by a new type of reinsurance contract that provides capital injections. To allow the insurance company's survival after ruin, the reinsurer injects capital only at ruin times…

Risk Management · Quantitative Finance 2018-06-13 Zied Ben Salah , José Garrido

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…

Probability · Mathematics 2018-07-02 Lioudmila Vostrikova , Jérôme Spielmann

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…

Probability · Mathematics 2017-03-08 Mohamed Amine Lkabous , Irmina Czarna , Jean-François Renaud

We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We extend the results in \cite{HJ15}, now in context of one-sided L\'evy risk models. We consider de…

Optimization and Control · Mathematics 2017-05-12 Camilo Hernandez , Mauricio Junca , Harold Moreno-Franco

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

This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and…

Risk Management · Quantitative Finance 2008-12-18 Jostein Paulsen

In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the…

Probability · Mathematics 2014-03-27 Chuancun Yin , Kam Chuen Yuen , Ying Shen

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…

Probability · Mathematics 2009-01-16 Florin Avram , Zbigniew Palmowski , Martijn R. Pistorius

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…

Mathematical Finance · Quantitative Finance 2017-06-27 Matija Vidmar

We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is…

Probability · Mathematics 2015-11-06 Harri Nyrhinen

We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…

Risk Management · Quantitative Finance 2013-08-26 Ilya Tkachev , Alessandro Abate

We investigate the role of reinsurance in maximizing the wealth of an insurance company. We use Liu's uncertainty theory (B. Liu, 2007) for the problem modeling and follow-up computations. The uncertainty measure of ruin for the insurance…

Optimization and Control · Mathematics 2021-01-19 Wrya Vakili , Alireza Ghaffari-Hadigheh

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…

Probability · Mathematics 2025-07-01 Oscar Peralta , Habacuq Vallejo

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

Applying excursion theory, we re-express several well studied fluctuation quantities associated to Parisian ruin problem for L\'evy risk processes in terms of integrals with respect to excursion measure for spectrally negative L\'evy…

Probability · Mathematics 2023-05-16 Bo Li , Xiaowen Zhou

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