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Risk processes connected with the compound poisson process
Scandinavian Actuarial Journal, 1969Abstract A portfolio of casualty insurances is usually very heterogeneous due to the wide spread of the individual risks also in case the policies are grouped according to risk classes. Stochastic models assuming identical risks for all policies in the risk class—e.g, the simple Poisson distribution—are not generally applicable to such a portfolio. For
Jung, Jan, Lundberg, Ove
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Empirical Likelihood for Compound Poisson Processes
Australian & New Zealand Journal of Statistics, 2012SummaryLet {N(t), t > 0} be a Poisson process with rate λ > 0, independent of the independent and identically distributed random variables with mean μ and variance . The stochastic process is then called a compound Poisson process and has a wide range of applications in, for example, physics, mining, finance and risk management.
Li, Z., Wang, X., Zhou, W.
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1991
One motivation for the model we develop in this chapter is provided by the atmospheric-noise data shown in Fig. 1.3. It is evident that a point process model can account for the occurrence times of the pulses. However, these times alone do not reflect all of the significant features. The amplitudes of the pulses exhibit wide variation and have a strong
Donald L. Snyder, Michael I. Miller
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One motivation for the model we develop in this chapter is provided by the atmospheric-noise data shown in Fig. 1.3. It is evident that a point process model can account for the occurrence times of the pulses. However, these times alone do not reflect all of the significant features. The amplitudes of the pulses exhibit wide variation and have a strong
Donald L. Snyder, Michael I. Miller
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On definition of compound poisson processes
Scandinavian Actuarial Journal, 1968Abstract Some authors define the (elementary) compound Poisson process in wide sense {χ t , 0 ⩽ t < ∞} with help of probability distributions where τ is a so-called operational time, a continuous non-decreasing function of t vanishing for t = 0, and V(q, t) is a non-negative distribution function for every t.
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1984
(a) Definitions Consideration is now extended from the claim number processes to processes which operate the claim amounts, concerning both the individual claims and their sums, the aggregate claims. A primary building block is the randomly varying size Z of an individual claim, i.e.
Robert Eric Beard +2 more
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(a) Definitions Consideration is now extended from the claim number processes to processes which operate the claim amounts, concerning both the individual claims and their sums, the aggregate claims. A primary building block is the randomly varying size Z of an individual claim, i.e.
Robert Eric Beard +2 more
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2018
This chapter reviews the basic facts about the simulation and inference for compound Poisson processes. Univariate and multivariate models are considered in full details. Full R code for completing the above analyses with yuima package is provided.
Stefano M. Iacus, Nakahiro Yoshida
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This chapter reviews the basic facts about the simulation and inference for compound Poisson processes. Univariate and multivariate models are considered in full details. Full R code for completing the above analyses with yuima package is provided.
Stefano M. Iacus, Nakahiro Yoshida
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Poisson processes and compound Poisson processes in insurance management [PDF]
Interdisciplinary Management Research, 2010 Some assumptions with respect to the number and the amount of damages are introduced in the paper. It will be assumed that the average of the number of damages is a Poisson process, which leads to a compound Poisson process for the total damages.
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Optimization methods for compound poisson risk processes
Cybernetics and Systems Analysis, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lyubchenko, G. I., Nakonechnyi, A. N.
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Point processes subordinated to compound Poisson processes
Theory of Probability and Mathematical Statistics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kobylych, K. V., Sakhno, L. M.
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Estimation for Compound Poisson Inarch Processes
2021REVSTAT-Statistical Journal, Vol. 19 No.
Gonçalves, E. +2 more
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