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We study the asymptotic behavior of ruin probabilities, as the initial reserve goes to infinity, for a reserve process model where claims arrive according to a renewal process, while between the claim times the process has the dynamics of…

Probability · Mathematics 2023-02-24 Ying He , Konstantin Borovkov

The main purpose of the paper is to study ruin probabilities in two discrete time risk models under rates of interest, where the premiums and claims are two independent sequences of m-dependent random variables, and the rate of interest is…

Probability · Mathematics 2025-08-21 Nguyen Huy Hoang , Tran Dinh Phung

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

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

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

This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the…

Applications · Statistics 2014-03-25 Salil Mehta

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

We reprove a result concerning certain ruin in the classical problem of the probability of ruin with risky investments and several of it's generalisations. We also provide the combined transition density of the risk and investment processes…

Probability · Mathematics 2008-12-02 David Maher

We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ($i=1,2,\dots$) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model…

Probability · Mathematics 2020-12-02 Onno Boxma , Esther Frostig , Zbigniew Palmowski

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

The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We…

Probability · Mathematics 2020-11-17 Yuri Kabanov , Nikita Pukhlyakov

This paper considers a variant of the classical Cram\'er-Lundberg model that is particularly appropriate in the credit context, with the distinguishing feature that it corresponds to a finite number of obligors. The focus is on computing…

Probability · Mathematics 2020-12-07 Guusje Delsing , Michel Mandjes

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 finite-time ruin probabilities for the compound Markov binomial risk model - a discrete-time model where claim sizes are modulated by a finite-state ergodic Markov chain. In the classic (non-modulated) case, the risk…

Probability · Mathematics 2025-07-23 Zbigniew Palmowski , Lewis Ramsden , Apostolos D. Papaioannou

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 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

Let $\textbf{Z}(t)=(Z_1(t) ,\ldots, Z_d(t))^\top , t \in \mathbb{R}$ where $Z_i(t), t\in \mathbb{R}$, $i=1,...,d$ are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For…

Probability · Mathematics 2021-10-27 Krzysztof Bisewski , Krzysztof Debicki , Nikolai Kriukov

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

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

Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak…

Probability · Mathematics 2020-06-05 Qianqian Zhou , Alexander Sakhanenko , Junyi Guo