Read e-book online Encyclopedia of Actuarial Science PDF

By Jozef Teugels, Bj?rn Sundt

ISBN-10: 0470846763

ISBN-13: 9780470846766

The Encyclopedia of Actuarial technology provides a well timed and finished physique of information designed to function an important reference for the actuarial career and all comparable company and monetary actions, in addition to researchers and scholars in actuarial technological know-how and similar parts. Drawing at the adventure of prime foreign editors and authors from and educational examine the encyclopedia offers an authoritative exposition of either quantitative equipment and sensible features of actuarial technology and assurance. The cross-disciplinary nature of the paintings is mirrored not just in its assurance of key techniques from enterprise, economics, hazard, likelihood thought and statistics but in addition by way of the inclusion of aiding issues equivalent to demography, genetics, operations examine and informatics.

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6) When ruin occurs caused by a claim, |U (T )| (or −U (T )) is called the severity of ruin or the deficit at the time of ruin, U (T −) (the left limit of U (t) at t = T ) is called the surplus immediately before the time of ruin, and [U (T −) + |U (T )|] is called the amount of the claim causing ruin (see Figure 1 of severity of ruin). It can be shown [1] that for u ≥ 0, ψ(u) = e−Ru , E[eR|U (T )| |T < ∞] (7) where R > 0 is the adjustment coefficient and −R is the negative root of Lundberg’s fundamental equation ∞ λ e−sx dP (x) = λ + δ − cs.

M. & Hipp, C. (2001). On the time to ruin for Erlang(2) risk process, Insurance: Mathematics and Economics 29, 333–344. M. R. (1991). Recursive calculation of survival probabilities, ASTIN Bulletin 21, 199–221. Dufresne, F. U. (1988). The probability and severity of ruin for combinations of exponential claim amount distributions and their translations, Insurance: Mathematics and Economics 7, 75–80. Dufresne, F. U. (1991). Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance: Mathematics and Economics 10, 51–59.

Sundt and Jewell’s family of discrete distributions, ASTIN Bulletin 18, 17–29. E. (2002). Compound geometric residual lifetime distributions and the deficit at ruin, Insurance: Mathematics and Economics 30, 421–438. , Drekic, S. & Cai, J. (2003). Equilibrium Compound Distributions and Stop-loss Moments, IIPR Research Report 03-10, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada. E. S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications, Lecture Notes in Statistics 156, Springer-Verlag, New York.

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

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