Generalized poisson models and their applications in insurance and finance
著者
書誌事項
Generalized poisson models and their applications in insurance and finance
(Modern probability and statistics)
VSP, 2002
大学図書館所蔵 全8件
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  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
目次
- Basic notions of probability theory random variables, their distributions and moments
- generating and characteristic functions
- random vectors
- stochastic independence
- weak convergence of random variables and distribution functions
- Poisson theorem
- law of large numbers
- central limit theorem
- stable laws
- the Berry-Esseen inequality
- asymptotic expansions in the central limit theorem
- elementary properties of random sums
- stochastic processes
- Poisson process
- the definition and elementary properties of a Poisson process
- Poisson process as a model of chaotic displacement of points in time
- the asymptotic normality of a Poisson process
- elementary rarefaction of renewal processes
- convergence of superpositions of independent stochastic processes
- characteristic features of the problem
- approximation of distributions of randomly indexed random sequences by special mixtures
- the transfer theorem
- relations between the limit laws for random sequences with random and non-random indices
- necessary and sufficient conditions for the convergence of distributions of random sequences with independent random indices
- convergence of distributions of randomly indexed sequences to identifiable location or scale mixtures
- the asymptotic behaviour of extremal random sums
- convergence of distributions of random sums
- the central limit theorem and the law of large numbers for random sums
- a general theorem on the asymptotic behaviour of superpositions of independent stochastic processes
- the transfer theorem for random sums of independent identically distributed random variables in the double array limit scheme
- compound Poisson distribution
- mixed and compound Poisson distributions
- discrete compound Poisson distributions
- the asymptotic normality of compound Poisson distributions
- the Berry-Esseen inequality for Poisson random sums
- non-central Lyapunov fractions
- asymptotic expansions for compound Poisson distributions
- the asymptotic expansions for the quantiles of compound Poisson distributions
- exponential inequalities for the probabilities of large derivations of Poisson random sums
- an analog of Bernshtein-Kolmogorov inequality
- the application of Esscher transforms to the approximation of the tails of compound Poisson distributions
- estimates of convergence rate in local limit theorems for Poisson random sums
- classical risk processes
- the definition of the classical risk process - its asymptotic normality
- the Pollaczek-Khinchin-Beekman formula for the ruin probability in the classical risk process
- approximations for the ruin probability with small safety loading
- asymptotic expansions for the ruin probability with small safety loading
- approximations for the ruin probability
- asymptotic approximations for the distributions of the surplus in general risk processes
- a problem of inventory control
- a non-classical problem of optimization of the initial capital
- doubly stochastic Poisson processes (Cox processes)
- the asymptotic behaviour of random sums
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