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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 study a multidimensional renewal risk model, with common counting process and cadlag returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly…

Probability · Mathematics 2024-12-18 Dimitrios G. Konstantinides , Charalampos D. Passalidis

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 study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…

Probability · Mathematics 2017-09-08 Ivana Geček Tuđen

The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We…

Probability · Mathematics 2007-05-23 R. A. Doney , R. A. Maller

In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider few versions of the ruin…

Probability · Mathematics 2021-10-05 Zbigniew Palmowski

In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain…

Probability · Mathematics 2013-03-22 Ronnie Loeffen , Irmina Czarna , Zbigniew Palmowski

We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics,…

Probability · Mathematics 2009-09-01 Jeffrey F. Collamore

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

For a L\'evy process $X$ on a finite time interval consider the probability that it exceeds some fixed threshold $x>0$ while staying below $x$ at the points of a regular grid. We establish exact asymptotic behavior of this probability as…

Probability · Mathematics 2022-01-05 Krzysztof Bisewski , Jevgenijs Ivanovs

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin…

Probability · Mathematics 2023-11-07 Denis Denisov , Niklas Gotthardt , Dmitry Korshunov , Vitali Wachtel

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

For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of…

Probability · Mathematics 2024-10-11 Yang Chen , Zhaolei Cui , Yuebao Wang

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

Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q…

Probability · Mathematics 2020-07-16 Spyridon M. Tzaninis , Nikolaos D. Macheras

In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…

Probability · Mathematics 2013-06-21 Jean-François Renaud

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 considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability…

Probability · Mathematics 2025-08-12 Viktor Antipov

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

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