Gerber shiu function

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August undefined, 2024

WebSep 7, 2024 · Abstract: We approximate Gerber–Shiu functions with heavy-tailed claims in a recently introduced risk model having both interclaim times and premiums depending on the claim sizes. We apply a ... WebIn this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient …

An introduction to Gerber-Shiu analysis - University of …

WebDownloadable (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 … 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 ... enya - orinoco flow lyrics

The Gerber-Shiu discounted penalty function: A review from …

WebGerber-Shiu penalty function of the process (4). Weak approximations in risk theory have been used in Iglehart (1969), Grandell (1977), and recently in Sarkar and Sen (2005) to obtain the Gerber-Shiu function for (3) in the case = 2, and in Furrer et al. (1997) to estimate ruin probabilities within a nite time horizon. 2 Preliminaries and main ... WebFor the new process we have auxiliary unknowns A i (x) representing ruin or survival probabilities (or, more generally, Gerber-Shiu functions) when starting at x conditioned on a phase i with drift downwards (i.e., in one of the “auxiliary stages of artificial time” introduced by changing the jumps to segments of slope − 1). WebJun 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. … drichardson509 yahoo.com

GERBER-SHIU FUNCTIONAL FOR THE CLASSICAL RISK …

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 … 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. enyart electric motorWebGerber-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 ... enyart electric motor service

"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. " - Gerber shiu function

Gerber shiu function

Risks Free Full-Text Recursive Approaches for Multi-Layer …

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 ... WebThis paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber–Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we establish a recursion method for computing the Gerber–Shiu expected discounted …

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WebJun 6, 2024 · In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate ...

http://qkxb.hut.edu.cn/zk/ch/reader/create_pdf.aspx?file_no=20100111&flag=1&journal_id=hngydxzrb&year_id=2010 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 ...

WebMar 1, 2024 · 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 … WebMay 1, 2024 · Estimating the Gerber–Shiu functions in the compound Poisson model: reference curves (red curves) and 25 estimated curves (green curves). (a) Ruin probability; (b) expected claim size causing ruin; (c) Laplace transform of ruin time. (For interpretation of the references to color in this figure legend, the reader is referred to the web ...

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

WebFeb 1, 2010 · The Gerber–Shiu function of the part due to a jump of {Z t} can be found in a similar way. Remark. In many papers, the Gerber–Shiu function is expressed through a defective renewal equation, see Gerber and Shiu (1998), Tsai and Willmot (2002) or Biffis and Morales (2008). This renewal equations are a direct consequence of the removing of ... enyart electric motor repair south bend inWebOct 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. drichardsinteriorsWebSep 8, 2024 · In this paper, we construct an estimator of the Gerber-Shiu function (2) in the compound Poisson model (1). As Zhang and Su (2024), our estimator is a projection … d richards interiorsWebThe 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 ... drichards onehealth.caWebBy 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 … d-richards cricketerWebMar 1, 2024 · 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 … drichardson indiantrailslibrary.orgWebMar 21, 2024 · Abstract: The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted … d. richardson