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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

This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram\'er-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost…

Probability · Mathematics 2026-04-01 Michel Denuit , José Miguel Flores-Contró , Christian Y. Robert

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

This paper deals with the discrete-time risk model with nonidentically distributed claims. We suppose that the claims repeat with time periods of three units, that is, claim distributions coincide at times $\{1,4,7,\ldots\}$, at times…

Probability · Mathematics 2016-01-07 Andrius Grigutis , Agneška Korvel , Jonas Šiaulys

Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…

Statistics Theory · Mathematics 2015-07-29 Jinzhu Li , Qihe Tang

We study the asymptotics of the ruin probability in the Cram\'er-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive…

Probability · Mathematics 2019-04-26 Frank Aurzada , Micha Buck

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

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

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 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 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

We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing…

Probability · Mathematics 2020-04-29 Peter Grandits , Maike Klein

We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…

Mathematical Finance · Quantitative Finance 2016-02-16 Gunther Leobacher , Michaela Szölgyenyi , Stefan Thonhauser

We consider the classical optimal dividends problem under the Cram\'er-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness…

Optimization and Control · Mathematics 2015-12-08 Camilo Hernandez , Mauricio Junca

In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time $T$ follows a normal distribution with a given mean and a given variance. In both…

Mathematical Finance · Quantitative Finance 2022-06-13 Katia Colaneri , Julia Eisenberg , Benedetta Salterini

We investigate the asymptotic of ruin probabilities when the company combines the life- and non-life insurance businesses and invests its reserve into a risky asset with stochastic volatility and drift driven by a two-state Markov process.…

Probability · Mathematics 2020-12-10 Anastasiya Ellanskaya , Yuri Kabanov

This paper considers a Cram\'er-Lundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claim-size distribution, and the premium rate, but we…

Probability · Mathematics 2019-06-10 Corina Constantinescu , Guusje Delsing , Michel Mandjes , Leonardo Rojas Nandayapa

The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric L\'evy process. Considering the ruin probability as a of the capital reserve we obtain for…

Probability · Mathematics 2024-01-10 Viktor Antipov , Yuri Kabanov

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

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. (2005) for such processes…

Probability · Mathematics 2007-09-07 K. A. Borovkov , D. C. M. Dickson