Fourier-cosine method for Gerber-Shiu functions [PDF]
Insurance: Mathematics and Economics, 2015 In this article, we provide a systematic study on effectively approximating the Gerber–Shiu functions, which is a hardly touched topic in the current literature, by incorporating the recently popular Fourier-cosine method.
Chau, KW, Yam, SCP, Yang, H
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The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions. [PDF]
Methodol Comput Appl Probab, 2023 AbstractIn this paper, we consider discounted penalty functions, also called Gerber-Shiu functions, in a Markovian shot-noise environment. At first, we exploit the underlying structure of piecewise-deterministic Markov processes (PDMPs) to show that these penalty functions solve certain partial integro-differential equations (PIDEs).
Pojer S, Thonhauser S.
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On the joint analysis of the total discounted payments to policyholders and shareholders: Dividend barrier strategy [PDF]
Risks, 2015 In the compound Poisson insurance risk model under a dividend barrier strategy, this paper aims to analyze jointly the aggregate discounted claim amounts until ruin and the total discounted dividends until ruin, which represent the insurer’s payments to ...
Cheung, ECK, Liu, H, Woo, JK
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Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process. [PDF]
ScientificWorldJournal, 2015 In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy process with certain positive jumps and arbitrary negative jumps.
Yin C, Yuen KC, Shen Y.
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The Gerber-Shiu expected discounted penalty-reward function under an affine jump-diffusion model [PDF]
ASTIN Bulletin, 2008 We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases,
Avram, Florin +1 more
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Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model [PDF]
Insurance: Mathematics and Economics, 2019 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 time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ...
Preischl, M., Thonhauser, S.
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On a discrete-time risk model with delayed claims and dividends [PDF]
, 2013 In this paper, we study the discounted free Gerber–Shiu function for the compound binomial risk model with by-claims and randomized dividend policy. Specifically, explicit expression for the discounted free Gerber–Shiu function is obtained.
Li, J, Wu, R, Yuen, KC
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The Gerber-Shiu discounted penalty function: A review from practical perspectives
Insurance: Mathematics and Economics, 2023 The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except ...
Yue He +3 more
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On the joint analysis of the total discounted payments to policyholders and shareholders: Threshold dividend strategy [PDF]
, 2016 In insurance risk theory, dividend and aggregate claim amount are of great research interest as they represent the insurance company's payments to its shareholders and policyholders respectively.
Cheung, ECK, Liu, H
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On a class of stochastic models with two-sided jumps [PDF]
, 2011 In this paper a stochastic process involving two-sided jumps and a continuous downward drift is studied. In the context of ruin theory, the model can be interpreted as the surplus process of a business enterprise which is subject to constant expense rate
Cheung, ECK
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