Gerber shiu function

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August undefined, 2024

WebFeb 26, 2024 · In this paper, we consider the risk model perturbed by a diffusion process. We assume an Erlang(n) risk process, (\(n=1,2,\ldots\)) to study the Gerber-Shiu discounted penalty function when ruin is due to claims or oscillations by including a dependence structure between claim sizes and their occurrence time.We derive the integro-differential … WebJun 28, 2016 · We perform analysis based on the Gerber–Shiu function introduced in Landriault et al. which extends the original Gerber–Shiu function by incorporating the number of claims until ruin into the analysis. We obtain some general results relating to finite time ruin problems on the assumption that the underlying risk process is a classical risk ...

(PDF) Estimating the Gerber-Shiu Function in a Compound …

WebMar 1, 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. Fourier-cosine method has been a prevailing numerical method in option pricing theory since the work of Fang and ... WebJan 1, 2024 · In particular, we find that the expected discounted penalty function introduced by Gerber and Shiu [1] has become a standard tool for analyzing ruin problems, and it is … blush cat emoji

An introduction to Gerber-Shiu analysis - University of …

Web湖南工业大学学报 Journal of Hunan University of Technology Vol.24 No.1 Jan.2010 第24卷第1期 2010年1月复合Poisson-Geometric过程的性质及简单应用蔡秋娥，廖基定 WebOct 22, 2011 · The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty … Michael R. Powers and Gerber and Shiu analyzed the behavior of the insurer's surplus through the expected discounted penalty function, which is commonly referred to as Gerber-Shiu function in the ruin literature and named after actuarial scientists Elias S.W. Shiu and Hans-Ulrich Gerber. It is arguable whether the … See more In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key … See more The theoretical foundation of ruin theory, known as the Cramér–Lundberg model (or classical compound-Poisson risk model, classical risk process or Poisson risk process) was introduced in 1903 by the Swedish actuary Filip Lundberg. Lundberg's work … See more • Financial risk • Volterra integral equation#Ruin theory See more • Gerber, H.U. (1979). An Introduction to Mathematical Risk Theory. Philadelphia: S.S. Heubner Foundation Monograph Series 8. • Asmussen S., Albrecher H. (2010). Ruin Probabilities, 2nd Edition. Singapore: World Scientific Publishing Co. See more E. Sparre Andersen extended the classical model in 1957 by allowing claim inter-arrival times to have arbitrary distribution functions. See more • Compound-Poisson risk model with constant interest • Compound-Poisson risk model with stochastic interest • Brownian-motion risk model See more cleveland browns 1st round draft history

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Fourier-cosine method for Gerber–Shiu functions - ScienceDirect

WebMar 1, 2013 · An explicit expression for the Gerber–Shiu function when u = z is obtained when the credit and debit interest rates are equal, and explicit results for the … WebOct 22, 2011 · It is established that the value-function is the unique stochastic solution and the pointwise smallest stochastic supersolution of the associated HJB equation. Furthermore, a necessary and sufficient condition is identified for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function. cleveland browns 1st round picks blush cbd gummies free trial

"WebDec 5, 2014 · Then the numerical evaluation of the finite-time Gerber-Shiu function is illustrated for three special choices of penalty function w, that could be applied to the … " - Gerber shiu function

Gerber shiu function

WebJan 1, 2014 · where \(w(x,y)\) is a (bounded) positive function and \(\alpha \ge 0\).This function has recently attracted great interest in research, also for more general models than the classical one. The discounted penalty at ruin, also called the Gerber–Shiu function, appears naturally in many applications.. Since the ruin probability does not take the time … Web对Gerber-Shiu折现罚金函数的研究是破产理论主要研究的问题之一，它为研究破产前瞬间资产余额和破产时赤字的联合密度提供了统一的方法.对此问题的研究始于Gerberand Shiu(1998)[3];Lin(2003)研究了时间间隔为Erlang(2);李平(2013)[4]研究了双Poisson风险模型下Gerber-Shiu函数.

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WebJun 20, 2024 · In this paper, we analyze the Gerber–Shiu discounted penalty function for a constant interest rate in delayed claim reporting times. Using the Poisson … WebThe Gerber–Shiu (G-S) function, first introduced in Gerber and Shiu , and other risk related quantities, such as the moments of the expected dividend payments have been extensively studied for the aforementioned models under the multi-layer dividend strategy based on a layer-by-layer recursive approach, for which certain disadvantages have ...

WebFeb 1, 2010 · The Expected Discounted Penalty Function (EDPF) was introduced in a series of now classical papers (Gerber and Shiu, 1997, Gerber and Shiu, 1998a, Gerber and Shiu, 1998b).Motivated by applications in option pricing and risk management, and inspired by recent developments in fluctuation theory for Lévy processes, we study an … WebGerber-Shiu Function; Lévy Processes; Ruin Theory; Back to top Reviews. From the book reviews: “The book under review gives a modern perspective on the problems in ruin theory in the framework of the classical Cramér-Lundberg risk model. … This compact book combines rigorous mathematical treatments with discussions and contains a ...

Web豆丁网是面向全球的中文社会化阅读分享平台，拥有商业,教育,研究报告,行业资料,学术论文,认证考试,星座,心理学等数亿实用 ... WebJul 7, 2024 · In this paper, we consider the compound Poisson risk model with stochastic premium income. We propose a new estimation of Gerber-Shiu function by an efficient method: Fourier-cosine series expansion.

WebJul 24, 2015 · Analytic expressions for the Gerber–Shiu expected discounted penalty function and the expected discounted tax payments until ruin are derived. The Cramér-Lundberg asymptotic formula is shown to hold true for the Gerber–Shiu function, and it differs from the case without tax by a multiplicative constant.

WebTo conclude, Chapter4introduces a generalized Gerber-Shiu function where the penalty function includes two additional random variables : the minimum surplus level before ruin X T, and the surplus immediately after the claim before the claim causing ruin R N T 1. This generalized Gerber-Shiu function, denoted as m (u), allows for the study of random blush causes rashWebJan 21, 2024 · As a preliminary of estimating the Gerber-Shiu function, we investigate its Fourier transform. Hereafter, we use L^1=L^1 (\mathbb {R}) and L^2=L^2 (\mathbb {R}) … cleveland browns 1st game 2022WebRemark 24. As may be easily checked, the ﬁrst expression for GZ1,δ(x) is the smooth Gerber-Shiu function ﬁtting the value of w(x) = xat 0, and also its derivative in the non-compound Poison model case. The second is a simpler expression, taking advantage of the non-unicity of the Gerber-Shiu function – see [APP15] and next section. Lemma 12. cleveland browns 2010 nfl draft picksWebDownloadable (with restrictions)! In this paper, we concern the statistical estimation of the Gerber-Shiu function under a risk model with stochastic premiums. We express the Gerber-Shiu function by Laguerre series expansion and estimate it based on observed information. Moreover, we study the convergence rate of our proposed estimator and … blush cbdWebJun 17, 2024 · In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when the surplus process is observed at a high frequency. … cleveland browns 2004 nfl draftWebBy introducing an auxiliary function, we provide a smooth extension of the Gerber–Shiu function, which has closed-form Fourier transform and is differentiable over the whole … blush cathedral veilWebAug 27, 2024 · The solutions to the two-sided exit problem and the Gerber–Shiu function at the draw-down Parisian ruin time are obtained in terms of the scale functions … cleveland browns 2010 season