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This note is an addendum to the work initiated by Eberlein, Kabanov, and Schmidt and developed further by Kabanov and Promyslov on the asymptotics of the ruin probabilities in the Sparre Andersen model with investments in a risky asset.…

Probability · Mathematics 2026-04-08 Yuri Kabanov , Danil Legenkiy , Platon Promyslov

In this paper, we generalise the results presented in the literature for the ruin probability for the insurer--reinsurer model under a pro-rata reinsurance contract. We consider claim amounts that are described by a phase-type distribution…

Mathematical Finance · Quantitative Finance 2023-03-15 Krzysztof Burnecki , Zbigniew Palmowski , Marek Teuerle , Aleksandra Wilkowska

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

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

The paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing a…

Probability · Mathematics 2023-11-21 Viktor Antipov , Yuri Kabanov

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

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

It has been decades since the academic world of ruin theory defined the insolvency of an insurance company as the time when its surplus falls below zero. This simplification, however, needs careful adaptions to imitate the real-world…

Risk Management · Quantitative Finance 2020-07-06 Aili Zhang , Ping Chen , Shuanming Li , Wenyuan Wang

The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite…

Risk Management · Quantitative Finance 2012-10-16 Rudi Schäfer , Alexander F. R. Koivusalo

In this paper we consider the Parisian ruin probabilities for the dual risk model in a discrete-time setting. By exploiting the strong Markov property of the risk process we derive a recursive expression for the fnite-time Parisian ruin…

Probability · Mathematics 2017-08-24 Zbigniew Palmowski , Lewis Ramsden , Apostolos D. Papaioannou

Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as…

Optimization and Control · Mathematics 2018-09-10 Michael Preischl , Stefan Thonhauser

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

Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform.…

Probability · Mathematics 2019-06-13 Persi Diaconis , Kelsey Houston-Edwards , Laurent Saloff-Coste

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 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

The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years. Although interesting in their own right,…

Risk Management · Quantitative Finance 2014-06-27 Zied Ben-Salah , Hélène Guérin , Manuel Morales , Hassan Omidi Firouzi

We present here a new extended model of the gambler's ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is…

Physics and Society · Physics 2018-10-23 Tomohisa Imai , Toru Ohira

In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an…

Probability · Mathematics 2022-09-02 Zbigniew Palmowski , Lewis Ramsden , Apostolos D. Papaioannou

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

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result,…

Risk Management · Quantitative Finance 2014-10-16 Lingjiong Zhu