By Jozef Teugels, Bj?rn Sundt
The Encyclopedia of Actuarial technology provides a well timed and finished physique of information designed to function a necessary reference for the actuarial career and all similar enterprise and fiscal actions, in addition to researchers and scholars in actuarial technology and similar components. Drawing at the event of major overseas editors and authors from and educational examine the encyclopedia offers an authoritative exposition of either quantitative tools and useful features of actuarial technological know-how and coverage. The cross-disciplinary nature of the paintings is mirrored not just in its assurance of key strategies from company, economics, probability, chance conception and information but in addition through the inclusion of aiding themes resembling demography, genetics, operations study and informatics.
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Moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process, North American Actuarial Journal 7(1), 1–12. E. (1996). Advanced Risk Theory: A SelfContained Introduction, Editions de l’Universite de Bruxelles, Brussels. E. & Marceau, E. (1996). Classical numerical ruin probabilities, Scandinavian Actuarial Journal 109–123. M. (1992). On the distribution of the surplus prior to ruin, Insurance: Mathematics and Economics 11, 191–207. M. (1994). Some comments on the compound binomial model, ASTIN Bulletin 24, 33–45.
Numerical values of compound Poisson distributions are easy to obtain using Panjer’s recursive formula k Pr{K = k} = fK (k) = a+b y=0 × fM (y)fK (k − y), βz 1+β . P2 (z) = β log 1 − 1+β log 1 − Pr{N = n}[P2 (z)]n y k k = 1, 2, 3, . . , (13) with a = 0 and b = λ, the Poisson parameter. It is also possible to use Panjer’s recursion to evaluate the distribution of the aggregate loss S = X1 + X2 + · · · + XN , (14) where the individual losses are also assumed to be independent and identically distributed, and to not depend on K in any way.
Ramaswami, V. (1999). Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, PA. H. (1980). The aggregate claims distribution and stop-loss reinsurance, Transactions of the Society of Actuaries 32, 523–535. H. (1981). Recursive evaluation of a family of compound distributions, ASTIN Bulletin 12, 22–26. H. E. (1992). Insurance Risk Models, Society of Actuaries, Schaumburg, IL. , Schmidt, V. & Teugels, J. (1999).