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Related papers: A ruin model with a resampled environment

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In this note we find a formula for the supremum distribution of spectrally positive or negative L\'evy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two…

Probability · Mathematics 2019-01-01 Zbigniew Michna

Consider a surplus process which both of collected premium and payed claim size are two independent compound Poisson processes. This article derives two approximated formulas for the ruin probability of such surplus process, say double…

Probability · Mathematics 2017-01-20 Amir T. Payandeh Najafabadi , Dan Kucerovsky

In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us…

Probability · Mathematics 2026-04-28 Spyridon M. Tzaninis , Apostolos Bozikas

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…

Probability · Mathematics 2022-06-28 Pavlina Jordanova , Evelina Veleva , Kosto Mitov

We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the…

Optimization and Control · Mathematics 2024-02-13 Salvatore Federico , Giorgio Ferrari , Maria-Laura Torrente

In this paper, we consider a classical risk model refracted at given level. We give an explicit expression for the joint density of the ruin time and the cumulative number of claims counted up to ruin time. The proof is based on solving…

Probability · Mathematics 2017-11-28 Yanhong Li , Zbigniew Palmowski , Chunming Zhao , Chunsheng Zhang

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an…

Probability · Mathematics 2015-03-19 Yuliya Mishura , Olena Ragulina , Oleksandr Stroyev

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance…

Probability · Mathematics 2007-11-16 Florin Avram , Zbigniew Palmowski , Martijn Pistorius

We analyze the general L\'{e}vy insurance risk process for L\'{e}vy measures in the convolution equivalence class $\mathcal{S}^{(\alpha)}$, $\alpha>0$, via a new kind of path decomposition. This yields a very general functional limit…

Probability · Mathematics 2012-08-22 Philip S. Griffin , Ross A. Maller

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 discuss the Cram\'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift $a$ and volatility $\sigma> 0.$ By assuming there is a cap on the claim sizes,…

Probability · Mathematics 2010-03-02 Shimao Fan , Sheng Xiong , Wei-Shih Yang

This paper studies an optimal investment-reinsurance problem for an insurer (she) under the Cram\'er--Lundberg model with monotone mean--variance (MMV) criterion. At any time, the insurer can purchase reinsurance (or acquire new business)…

Portfolio Management · Quantitative Finance 2024-05-30 Xiaomin Shi , Zuo Quan Xu

We study the default risk in incomplete information. That means, we model the value of a firm by one L\'evy process which is the sum of brownian motion with drift and compound Poisson process. This L\'evy process can not be observed…

Probability · Mathematics 2014-11-25 Waly Ngom

In the setting of a L\'evy insurance risk process, we present some results regarding the Parisian ruin problem which concerns the occurrence of an excursion below zero of duration bigger than a given threshold $r$. First, we give the joint…

Probability · Mathematics 2017-11-15 Ronne Loeffen , Zbigniew Palmowski , Budhi Surya

In this paper we consider some generalizations of the classical d-dimensional Brownian risk model. This contribution derives some non-asymptotic bounds for simultaneous ruin probabilities of interest. In addition, we obtain non-asymptotic…

Probability · Mathematics 2022-05-17 Nikolai Kriukov

In this paper a class of Ornstein--Uhlenbeck processes driven by compound Poisson processes is considered. The jumps arrive with exponential waiting times and are allowed to be two-sided. The jumps are assumed to form an iid sequence with…

Probability · Mathematics 2016-09-01 Anders Rønn-Nielsen

In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.

Probability · Mathematics 2016-08-22 Peng Liu , Chunsheng Zhang , Lanpeng Ji

In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance…

Computational Finance · Quantitative Finance 2013-08-15 Hansjörg Albrecher , Corina Constantinescu , Zbigniew Palmowski , Georg Regensburger , Markus Rosenkranz

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common…

Probability · Mathematics 2017-05-30 Hui Xu , Fengyang Cheng

We consider two-dimensional L\'evy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that…

Probability · Mathematics 2024-03-25 Vladimir Fomichov , Sandro Franceschi , Jevgenijs Ivanovs