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On the approximation of functions satisfying defective renewal equations [PDF]
Journal of Computational and Applied Mathematics, 2011 Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don't admit a explicit expression. In this work we consider to approximate them by means of a gamma-type operator given in terms of the Laplace transform of the initial function.
C. Sangüesa
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A generalized defective renewal equation for the surplus process perturbed by diffusion
Insurance: Mathematics and Economics, 2002 The authors consider the surplus process \(V(t)= u+ ct- S(t)+\sigma W(t)\), \(t\geq 0\), where \(\sigma> 0\), \(\{W(t): t\geq 0\}\) is a standard Wiener process, that is independent of the compound Poisson process \(\{S(t): t\geq 0\}\). The defective renewal equation for the expected discounted function of a penalty at the time of ruin is generalized ...
Gordon Willmot, Cary Chi-Liang Tsai
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Asymptotics for the Solutions to Defective Renewal Equations [PDF]
Abstract and Applied Analysis, 2014 This paper investigates the defective renewal equations under the nonconvolution equivalent distribution class. The asymptotics of the solution to the defective renewal equations have been given for the heavy-tailed and light-tailed cases, respectively.
Kaiyong Wang, Yang Chen, Zhongquan Tan
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On the discounted penalty function in the discrete time stationary renewal risk model [PDF]
Journal of Computational and Applied Mathematics, 2010 In this paper we consider the discrete time stationary renewal risk model. We express the Gerber–Shiu discounted penalty function in the stationary renewal risk model in terms of the corresponding Gerber–Shiu function in the ordinary model. In particular,
Z. Bao, Jing Wang
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A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model
Mathematics, 2019 In this paper, we propose a new generalized Gerber−Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time.
Jiechang Ruan +5 more
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The ruin problem in a renewal risk model with two-sided jumps
Mathematical and Computer Modelling, 2013 Hua Dong, Zaiming Liu
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On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula
Scandinavian Actuarial Journal, 2014 Spyridon Vrontos +1 more
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On an Erlang(2) Process with Dependence Structure between Interclaim Arrivals and Claim Sizes
Asian Journal of Probability and Statistics, 2022 This paper considers an extension to the classical compound Poisson risk model for which an Erlang(2) process is utillized to the dependence structure between the claim sizes and interclaim times.
Qiao Li, Z. Bao
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Probability Risk Model of Claim Amount Affected by a Threshold Value
Asian Journal of Probability and Statistics, 2022 In this paper, we consider a new risk model of claim amount affected by a threshold value. The comparision between the claim interval and the threshold will affect the distribution of claims.
Qiao Li, Z. Bao
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Nonlinear Analysis, 2011 We investigate the asymptotic behavior of the Gerber–Shiu discounted penalty function ɸ(u) = E(e−δT 1{T
Jelena Kočetova, Jonas Šiaulys
doaj