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150325s1990 xx |||||o 00| ||eng c |
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|a (DE-627)JST081536917
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|a (JST)2101954
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|a DE-627
|b ger
|c DE-627
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|a eng
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|a 34E20
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|a Peters, Craig Steven
|e verfasserin
|4 aut
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|a New Methods for the Problem of Collective Ruin
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|c 1990
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
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|a The problem of "collective ruin" arises in a number of different situations in operations research and is particularly well suited as a model of risk business such as an insurance company. The problem of collective ruin is formulated in terms of dynamical stochastic processes for a risk reserve Z(t). The reserve grows according to a deterministic process β(Z(t)), the insurance premiums, and is decremented according to a compound stochastic process, claims. The integral-differential-difference equation is derived for the probability of survival to time t and a number of different methods for the solution of the stationary version of the equation, which corresponds to probability of surviving forever, are described. In particular, asymptotic techniques are developed based on the WKB method and its extensions for the solution of a broad class of risk problems. This greatly extends the classical work of Feller, Cramer, and others who were only able to treat the case in which β(Z(t)) is constant.
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|a Copyright 1990 Society for Industrial and Applied Mathematics
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|a asymptotic approximations
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|a WKB method
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|a turning point
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|a collective ruin
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|a Philosophy
|x Metaphysics
|x Etiology
|x Determinism
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| 650 |
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|a Economics
|x Economic disciplines
|x Financial economics
|x Insurance
|x Insurance expenses
|x Insurance premiums
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| 650 |
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|a Mathematics
|x Pure mathematics
|x Calculus
|x Differential calculus
|x Differential equations
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| 650 |
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|a Mathematics
|x Mathematical expressions
|x Mathematical functions
|x Mathematical transformations
|x Integral transformations
|x Laplace transformation
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| 650 |
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|a Mathematics
|x Mathematical procedures
|x Approximation
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| 650 |
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|a Business
|x Business engineering
|x Business risks
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| 650 |
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|a Business
|x Industry
|x Industrial sectors
|x Service industries
|x Insurance industry
|x Insurance providers
|x Insurance companies
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| 650 |
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|a Economics
|x Economic disciplines
|x Financial economics
|x Insurance
|x Insurance expenses
|x Insurance premiums
|x Risk premiums
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| 650 |
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Algebra
|x Coefficients
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|a research-article
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1 |
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|a Mangel, Marc
|e verfasserin
|4 aut
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|i Enthalten in
|t SIAM Journal on Applied Mathematics
|d Society for Industrial and Applied Mathematics, 1966
|g 50(1990), 5, Seite 1442-1456
|w (DE-627)266884121
|w (DE-600)1468266-7
|x 00361399
|7 nnns
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|g volume:50
|g year:1990
|g number:5
|g pages:1442-1456
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|u https://www.jstor.org/stable/2101954
|3 Volltext
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|a AR
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|d 50
|j 1990
|e 5
|h 1442-1456
|