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Non-life Insurance Mathematics
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Models for the Claim Number Process
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insurance mathematics, statistical inference, poisson process, homogeneous poisson, the cramer
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1.http://thecramer.com/require attention [no title tag] anchor text Non-life insurance Mathematics
2.require attention [use absolute path for links] /collective-risk-modelsrequire attention [no title tag] anchor text Collective Risk Models
3.require attention [use absolute path for links] /models-for-the-claim-number-processrequire attention [no title tag] anchor text Models for the Claim Number Process
4.require attention [use absolute path for links] /the-total-claim-amountrequire attention [no title tag] anchor text The Total Claim Amount
5.require attention [use absolute path for links] /the-total-claim-amount/101-the-order-of-magnitude-of-the-total-claim-amountrequire attention [no title tag] anchor text The Order of Magnitude of the Total Claim Amount
6.require attention [use absolute path for links] /the-total-claim-amount/100-mixture-distributions-require attention [no title tag] anchor text Mixture distributions
7.require attention [use absolute path for links] /the-total-claim-amount/99-some-realistic-claim-size-require attention [no title tag] anchor text Some realistic claim size
8.require attention [use absolute path for links] /the-total-claim-amount/98-claim-number-process-require attention [no title tag] anchor text Claim number process
9.require attention [use absolute path for links] /models-for-the-claim-number-process/97-order-statistics-propertyrequire attention [no title tag] anchor text Order statistics property
10.require attention [use absolute path for links] /models-for-the-claim-number-process/96-cox-process-require attention [no title tag] anchor text Cox process
11.require attention [use absolute path for links] /models-for-the-claim-number-process/95-the-negative-binomial-process-as-mixed-poisson-processrequire attention [no title tag] anchor text The negative binomial process as mixed Poisson process
12.require attention [use absolute path for links] /models-for-the-claim-number-process/94-the-mixed-poisson-processrequire attention [no title tag] anchor text The Mixed Poisson Process
13.require attention [use absolute path for links] /models-for-the-claim-number-process/93-renewal-equation-of-the-form-require attention [no title tag] anchor text Renewal equation of the form
14.require attention [use absolute path for links] /models-for-the-claim-number-process/92-recurrence-times-of-a-renewal-processrequire attention [no title tag] anchor text Recurrence times of a renewal process
15.require attention [use absolute path for links] /models-for-the-claim-number-process/54-the-homogeneous-poisson-process-the-intensity-function-the-cramer-lundberg-modelrequire attention [no title tag] anchor text The Homogeneous Poisson Process the Intensity Function the Cramer-Lundberg Model
16.require attention [use absolute path for links] /collective-risk-models/49-statistical-inference-require attention [no title tag] anchor text Statistical inference
17.require attention [use absolute path for links] /collective-risk-models/47-the-claim-number-processrequire attention [no title tag] anchor text The claim number process
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19.require attention [use absolute path for links] /collective-risk-models/50-poisson-process-require attention [no title tag] anchor text Poisson process
20.require attention [use absolute path for links] /collective-risk-models/46-the-basic-modelrequire attention [no title tag] anchor text The Basic Model
21.require attention [use absolute path for links] /collective-risk-models/51-a-major-building-block-require attention [no title tag] anchor text A major building block
22.require attention [use absolute path for links] /models-for-the-claim-number-process/55-a-homogeneous-poisson-process-with-intensityrequire attention [no title tag] anchor text A homogeneous Poisson process with intensity
23.require attention [use absolute path for links] /models-for-the-claim-number-process/57-the-cramer-lundberg-modelrequire attention [no title tag] anchor text The Cramer-Lundberg model
24.require attention [use absolute path for links] /models-for-the-claim-number-process/58-the-markov-propertyrequire attention [no title tag] anchor text The Markov Property
25.require attention [use absolute path for links] /collective-risk-models/46-the-basic-modelrequire attention [no title tag] anchor text Read more...
26.require attention [use absolute path for links] /collective-risk-models/47-the-claim-number-processrequire attention [no title tag] anchor text Read more...
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Non-life insurance Mathematics Main Menu Non-life insurance MathematicsCollective Risk ModelsModels for the Claim Number ProcessThe Total Claim Amount Latest News The Order of Magnitude of the Total Claim Amount Mixture distributions Some realistic claim size Claim number process Order statistics property Cox process The negative binomial process as mixed Poisson process The Mixed Poisson Process Renewal equation of the form Recurrence times of a renewal process Popular The Homogeneous Poisson Process the Intensity Function the Cramer-Lundberg Model Statistical inference The claim number process The corresponding sample path Poisson process The Basic Model A major building block A homogeneous Poisson process with intensity The Cramer-Lundberg model The Markov Property Who s Online We have 37 guests online The Basic Model Written by theoretic In 1903 the Swedish actuary Filip Lundberg [55] laid the foundations of modern risk theory. Risk theory is a synonym for non-life insurance mathematics which deals with the modeling of claims that arrive in an insurance business and which gives advice on how much premium has to be charged in order to avoid bankruptcy ruin of the insurance company. Read more... The claim number process Written by theoretic The iid property of the claim sizes Xi reflects the fact that there is a homogeneous probabilistic structure in the portfolio. The assumption that claim sizes and claim times be independent is very natural from an intuitive point of view. But the independence of claim sizes and claim arrivals also makes the life of the mathematician much easier i.e. this assumption is made for mathematical convenience and tractability of the model. Now we can define the claim number process Read more... The corresponding sample path Written by theoretic In Figure 1.0.1 we see a sample path of the process N and the corresponding sample path of the compound sum process S. Both paths jump at the same times Ti by 1 for N and by Xi for S. Read more... Statistical inference User Rating 1 PoorBest Written by theoretic Although statistical inference on the processes S and N is utterly important for the insurance business we do not address this aspect in a rigorous way. The statistical analysis of insurance data is not different from standard statistical methods which have been developed for iid data and for counting processes. Read more... Poisson process Written by theoretic This concerns the renewal process which is considered in Section 2.2. It allows for more flexibility in choosing the distribution of the inter-arrival times Ti —Ti-\. But one has to pay a price in contrast to the Poisson process when N t has a Poisson distribution for every t this property is in general not valid for a renewal process. Moreover the distribution of N t is in general not known. Read more... A major building block Written by theoretic A major building block of classical risk theory is devoted to the probability of ruin; see Chapter 4. It is a global measure of the risk one encounters in a portfolio over a long time horizon. We deal with the classical small claim case and give the celebrated estimates of Cram´er and Lundberg Sections 4.2.1 and 4.2.2 . Read more... The Poisson Process Written by theoretic In this section we consider the most common claim number process the Poisson process. It has very desirable theoretical properties. For example one can derive its finite-dimensional distributions explicitly. Read more... Definition 2.1.1 Written by theoretic A stochastic process N = N t t>o is said to be a Poisson process if the following conditions hold 1 The process starts at zero N 0 = 0 a.s. Read more... The Homogeneous Poisson Process the Intensity Function the Cramer-Lundberg Model Written by theoretic The most popular Poisson process corresponds to the case of a linear mean value function л x t = At t > 0 for some A > 0. A process with such a mean value function is said to be homogeneous inhomogeneous otherwise. The quantity A is the intensity or rate of the homogeneous Poisson process. If A = 1 N is called standard homogeneous Poisson process. Read more... « StartPrev1234567NextEnd » Page 1 of 7 Non-life insurance Mathematics Powered by Joomla Copyright 2009.All rights reserved.
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