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  • 1
    Book
    Book
    Lundberg approximations for compound distributions with insurance applications / (2001)
    New York [u.a.] :Springer,
    Details
    UID:
    almahu_BV013475845
    Format: X, 250 S.
    ISBN: 0-387-95135-0
    Series Statement: Lecture notes in statistics 156
    Language: English
    Subjects: Mathematics
    RVK:
    SI 856
    RVK:
    SK 800
    Keywords: Zusammengesetzte Verteilung ; Approximation
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009196439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    URL: Inhaltsverzeichnis
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
    Author information: Willmot, Gordon E., 1957-
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  • 2
    Online Resource
    Online Resource
    Lundberg Approximations for Compound Distributions with Insurance Applications (2001)
    New York, NY :Springer New York :
    Details
    UID:
    almahu_9947362962202882
    Format: X, 250 p. , online resource.
    ISBN: 9781461301110
    Series Statement: Lecture Notes in Statistics, 156
    Content: These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is induc­ tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis­ tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo­ nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed.
    Note: 1 Introduction -- 2 Reliability background -- 2.1 The failure rate -- 2.2 Equilibrium distributions -- 2.3 The residual lifetime distribution and its mean -- 2.4 Other classes of distributions -- 2.5 Discrete reliability classes -- 2.6 Bounds on ratios of discrete tail probabilities -- 3 Mixed Poisson distributions -- 3.1 Tails of mixed Poisson distributions -- 3.2 The radius of convergence -- 3.3 Bounds on ratios of tail probabilities -- 3.4 Asymptotic tail behaviour of mixed Poisson distributions -- 4 Compound distributions -- 4.1 Introduction and examples -- 4.2 The general upper bound -- 4.3 The general lower bound -- 4.4 A Wald-type martingale approach -- 5 Bounds based on reliability classifications -- 5.1 First order properties -- 5.2 Bounds based on equilibrium properties -- 6 Parametric Bounds -- 6.1 Exponential bounds -- 6.2 Pareto bounds -- 6.3 Product based bounds -- 7 Compound geometric and related distributions -- 7.1 Compound modified geometric distributions -- 7.2 Discrete compound geometric distributions -- 7.3 Application to ruin probabilities -- 7.4 Compound negative binomial distributions -- 8 Tijms approximations -- 8.1 The asymptotic geometric case -- 8.2 The modified geometric distribution -- 8.3 Transform derivation of the approximation -- 9 Defective renewal equations -- 9.1 Some properties of defective renewal equations -- 9.2 The time of ruin and related quantities -- 9.3 Convolutions involving compound geometric distributions -- 10 The severity of ruin -- 10.1 The associated defective renewal equation -- 10.2 A mixture representation for the conditional distribution -- 10.3 Erlang mixtures with the same scale parameter -- 10.4 General Erlang mixtures -- 10.5 Further results -- 11 Renewal risk processes -- 11.1 General properties of the model -- 11.2 The Coxian-2 case -- 11.3 The sum of two exponentials -- 11.4 Delayed and equilibrium renewal risk processes -- Symbol Index -- Author Index.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387951355
    Language: English
    DOI: 10.1007/978-1-4613-0111-0
    URL: http://dx.doi.org/10.1007/978-1-4613-0111-0
    URL: Volltext
    URL: Volltext  (lizenzpflichtig)
    URL: Inhaltstext
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  • 3
    Online Resource
    Online Resource
    Introductory stochastic analysis for finance and insurance / (2006)
    Hoboken, N.J. :John Wiley,
    Details
    UID:
    almafu_9959328700602883
    Format: 1 online resource (xvi, 224 pages) : , illustrations
    ISBN: 0471716421 , 9780471716426 , 0471793213 , 9780471793212 , 0471793205 , 9780471793205 , 1280411503 , 9781280411502
    Series Statement: Wiley series in probability and statistics
    Content: Aimed at actuaries who would like to learn stochastic modeling techniques, this is an introductory level book on stochastic analysis for finance. It introduces the basic theories of stochastic processes and stochastic calculus, and provides the tool kits for modeling and pricing in finance and insurance.
    Note: Overview of probability theory -- Discrete-time stochastic processes -- Continuous-time stochastic processes -- Stochastic calculus : basic topics -- Stochastic calculus : advanced topics -- Applications in insurance.
    Additional Edition: Print version: Lin, X. Sheldon. Introductory stochastic analysis for finance and insurance. Hoboken, N.J. : John Wiley, ©2006 ISBN 0471716421
    Language: English
    Keywords: Electronic books. ; Electronic books. ; Electronic books.
    DOI: 10.1002/0471793213
    URL: https://onlinelibrary.wiley.com/doi/book/10.1002/0471793213
    URL: https://onlinelibrary.wiley.com/doi/book/10.1002/0471793213
    URL: https://onlinelibrary.wiley.com/doi/book/10.1002/0471793213
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    Online Resource
    Open Access Request
    HU Berlin
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  • 4
    Online Resource
    Online Resource
    Introductory stochastic analysis for finance and insurance / (2006)
    Hoboken, N.J. :John Wiley,
    Details
    UID:
    almahu_9948196733702882
    Format: 1 online resource (xvi, 224 pages) : , illustrations
    ISBN: 0471716421 , 9780471716426 , 0471793213 , 9780471793212 , 0471793205 , 9780471793205 , 1280411503 , 9781280411502
    Series Statement: Wiley series in probability and statistics
    Content: Aimed at actuaries who would like to learn stochastic modeling techniques, this is an introductory level book on stochastic analysis for finance. It introduces the basic theories of stochastic processes and stochastic calculus, and provides the tool kits for modeling and pricing in finance and insurance.
    Note: Overview of probability theory -- Discrete-time stochastic processes -- Continuous-time stochastic processes -- Stochastic calculus : basic topics -- Stochastic calculus : advanced topics -- Applications in insurance.
    Additional Edition: Print version: Lin, X. Sheldon. Introductory stochastic analysis for finance and insurance. Hoboken, N.J. : John Wiley, ©2006 ISBN 0471716421
    Language: English
    Keywords: Electronic books.
    DOI: 10.1002/0471793213
    URL: https://onlinelibrary.wiley.com/doi/book/10.1002/0471793213
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    HU Berlin
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