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Distribution of shifted discrete random walk generated by distinct random variables and applications in ruin theory [PDF]
Modern Stochastics: Theory and ApplicationsIn this paper, the distribution function \[ \varphi (u)=\mathbb{P}\Bigg(\underset{n\geqslant 1}{\sup }{\sum \limits_{i=1}^{n}}({X_{i}}-\kappa )\lt u\Bigg),\] and the generating function of $\varphi (u+1)$ are set up.
Simonas Gervė, Andrius Grigutis
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A Heuristic Review of some Ruin Theory Results [PDF]
ASTIN Bulletin, 1985 AbstractThe paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recursion formula for computation of the aggregate claims distribution is noted and discussed.
Greg Taylor
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On capital allocation for a risk measure derived from ruin theory [PDF]
Insurance: Mathematics and Economics, 2022 This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given threshold.
Guusje Delsing +3 more
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On real growth and run-off companies in insurance ruin theory [PDF]
arXiv, 2015 We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is allowed to increase or decrease. In the latter case, the study is focused on run-off companies.
Harri Nyrhinen
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Some optimization and decision problems in proportional reinsurance [PDF]
Rect@, 2016 Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of ...
Castañer, Anna +2 more
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High order expansions for renewal functions and applications to ruin theory [PDF]
The Annals of Applied Probability, 2017 Comment: Annals of Applied Probability, Institute of Mathematical Statistics (IMS ...
Clément Dombry, Landy Rabehasaina
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Determining Safe Withdrawal Rates for Post-Retirement via a Ruin-Theory Approach [PDF]
RisksTo ensure a comfortable post-retirement life and the ability to cover living expenses, it is of utmost importance for individuals to have a clear understanding of how long their pre-retirement savings will last.
Diba Daraei, Kristina Sendova
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On the risk consistency and monotonicity of ruin theory [PDF]
European Actuarial Journal, 2021 Setting a proper minimum capital requirement is one of the most fundamental problems in the insurance industry. Ruin theory proposes a solution to this problem by identifying the minimum capital that a company needs to hold in order to stay solvent with a high probability. In this note we discuss the ruin theory risk consistency. More precisely we show
Hirbod Assa, Corina Constantinescu
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Sophisticated gamblers ruin and survival chances [PDF]
, 2013 This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy.
Mehta, Salil
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International Journal of Mathematics for Industry, 2023 This paper studies the Gerber–Shiu function for the insurance surplus process with additional investment under the Bachelier model. The Gerber–Shiu function allows us to study the moments of the time of ruin, which is the first time that the surplus is ...
Sutipon Punaluek, Yuri Imamura
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