Gerber-Shiu analysis with a generalized penalty function
, 2010 A generalization of the usual penalty function is proposed, and a defective renewal equation is derived for the Gerber-Shiu discounted penalty function in the classical risk model. This is used to derive the trivariate distribution of the deficit at ruin,
Woo, JK +3 more
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The calculation of gerber-shiu penalty function for pareto claims. [PDF]
, 2011 In this paper we consider Gerber-Shiu discounted penalty function in the classical risk model for Pareto claims. Our main goal is to construct an algorithm for obtaining values of the discounted penalty function (considering penalty function w=1). Due to
Janušauskas, Arūnas,
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On the time value of ruin in the discrete time risk model [PDF]
, 2002 Using an approach similar to that of Gerber and Shiu (1998), a recursive formula is given for the expected discounted penalty due at ruin, in the discrete time risk model. With it the joint distribution of three random variables is obtained; time to ruin,
Garrido, José, Li, Shuanming
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On a Gerber–Shiu type function and its applications in a dual semi-Markovian risk model [PDF]
, 2014 In this paper, we consider a dual risk process which can be used to model the surplus of a business that invests money constantly and earns gains randomly in both time and amount.
Liu, L, Cheung, ECK
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The Gerber-Shiu expected discounted penalty-reward function under an affine jump-diffusion model. [PDF]
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).
Avram, Florin, Usábel, Miguel A.
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An introduction to Gerber-Shiu analysis [PDF]
, 2011 A valuable analytical tool to understand the event of ruin is a Gerber-Shiu discounted penalty function. It acts as a unified means of identifying ruin-related quantities which may help insurers understand their vulnerability ruin.
Huynh, Mirabelle
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A numerical method for the expected penalty–reward function in a Markov-modulated jump–diffusion process. [PDF]
A generalization of the Cramér–Lundberg risk model perturbed by a diffusion is proposed. Aggregate claims of an insurer follow a compound Poisson process and premiums are collected at a constant rate with additional random fluctuation.
Usábel, Miguel A., Diko, Peter
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The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions. [PDF]
Methodol Comput Appl Probab, 2023 Pojer S, Thonhauser S.
europepmc +1 more source
Catastrophic risks and the pricing of catastrophe equity put options. [PDF]
Comput Manag Sci, 2021 Arnone M +3 more
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Computing Gerber-Shiu function in the classical risk model with interest using collocation method
, 2023 The Gerber-Shiu function is a classical research topic in actuarial science.However, exact solutions are only available in the literature for very specific cases where the claim amounts follow distributions such as the exponential distribution.
Zhang, Lianzeng, Yu, Zan
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