Gerber shiu function
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. WebAug 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 associated with the underlying spectrally negative Lévy process. Motivated by Baurdoux et al. (J Appl Probab 53:572–584, 2016) and Wang and Zhou (Appl Probab 52:1–33, 2024), in this ...
Gerber shiu function
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WebThis paper studies the statistical estimation of the Gerber-Shiu discounted penalty functions in a general spectrally negative Lévy risk model. Suppose that the claims process and the surplus process can be observed at a sequence of discrete time points. Using the observed data, the Gerber-Shiu functions are estimated by the Laguerre … 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 …
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 ... http://qkxb.hut.edu.cn/zk/ch/reader/create_pdf.aspx?file_no=20100111&flag=1&journal_id=hngydxzrb&year_id=2010
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 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. …
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 ...
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 … lowes rolling garage storageWeb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 lowes rolling plant standWeb5.4 Gerber–Shiu Measure and Gambler’s Ruin. We now have all the tools we need to provide a characterisation of the Gerber–Shiu measure ( 1.6) in terms of scale … lowes roll insulationWebThe 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 ... james webb space telescope cryocoolerWebDownloadable (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 … james webb space telescope first photoWebBy 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 … lowes roller coversWebAug 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 … lowes rollators