Download Encyclopedia of Actuarial Science by Jozef Teugels, Bj?rn Sundt PDF

By Jozef Teugels, Bj?rn Sundt

The Encyclopedia of Actuarial technology offers a well timed and entire physique of data designed to function a necessary reference for the actuarial occupation and all similar company and monetary actions, in addition to researchers and scholars in actuarial technology and comparable parts. Drawing at the event of top overseas editors and authors from and educational learn the encyclopedia presents an authoritative exposition of either quantitative tools and functional points of actuarial technology and assurance. The cross-disciplinary nature of the paintings is mirrored not just in its insurance of key ideas from company, economics, probability, likelihood thought and records but in addition via the inclusion of helping subject matters reminiscent of demography, genetics, operations learn and informatics.

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Xn ) through its support. A support of a random vector X is a set A ⊆ n for which Prob[ X ∈ A] = 1. Definition 2 (Comonotonic random vector) A random vector X = (X1 , . . , Xn ) is comonotonic if it has a comonotonic support. From the definition, we can conclude that comonotonicity is a very strong positive dependency structure. Indeed, if x and y are elements of the (comonotonic) support of X, that is, x and y are possible outcomes of X, then they must be ordered componentwise. This explains why the term comonotonic (common monotonic) is used.

N) exist such that d X= (f1 (Z), f2 (Z), . . , fn (Z)). (3) From (1) we see that, in order to find the probability of all the outcomes of n comonotonic risks Xi being less than xi (i = 1, . . , n), one simply takes the probability of the least likely of these n events. It is obvious that for any random vector (X1 , . . , Xn ), not necessarily comonotonic, the following inequality holds: Prob[X1 ≤ x1 , . . , Xn ≤ xn ] ≤ min FX1 (x1 ), . . , FXn (xn ) , (4) and since Hoeffding [7] and Fr´echet [5], it is known that the function min{FX1 (x1 ), .

2001). Modern Actuarial Risk Theory, Kluwer, Dordrecht. , Van Heerwaarden, A. & Goovaerts, M. (1994). Ordering of Actuarial Risks, Institute for Actuarial Science and Econometrics, Amsterdam. [10] Nelsen, R. (1999). An Introduction to Copulas, Springer, New York. [11] Vyncke, D. (2003). D. Thesis, Katholieke Universiteit Leuven, Leuven. [12] Wang, S. & Dhaene, J. (1998). Comonotonicity, correlation order and stop-loss premiums, Insurance: Mathematics and Economics 22, 235–243. (See also Claim Size Processes; Risk Measures) DAVID VYNCKE Compound Distributions Let N be a counting random variable with probability function qn = Pr{N = n}, n = 0, 1, 2, .

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