×

Concerning the use of Laguerre polynomials for inversion of Laplace transforms in risk theory. (English) Zbl 0367.60020


MSC:

60E05 Probability distributions: general theory
62P05 Applications of statistics to actuarial sciences and financial mathematics
44A10 Laplace transform
Full Text: DOI

References:

[1] Beekman, J. A., A ruin function approximation. Transactions of the Society of Actuaries 21, 41–48, 275–279 (1969).
[2] Bowers, N. L., jr., Expansion of probability density functions as a sum of gamma densities with applications to risk theory. Transactions of the Society of Actuaries 18, 125–147 (1966).
[3] Bühlmann, H., Mathematical methods in risk theory. Springer-Verlag, 1970. · Zbl 0209.23302
[4] Cramér, H., Collective risk theory. A survey of the theory from the point of view of the theory of stochastic processes. Skandia Insurance Company, 1955.
[5] Kuller, R. G., Topics in modern analysis. Prentice-Hall Inc., 1969. · Zbl 0198.47602
[6] Pfenninger, F., Eine neue Methode zur Berechnung der Ruinwahrscheinlichkeit mittels Laguerre-Entwicklung. Blätter der DGVM 11, 491–532 (1974). · Zbl 0321.62107 · doi:10.1007/BF02809740
[7] Seal, H. L., Stochastic theory of a risk business. John Wiley and Sons, Inc., 1969. · Zbl 0196.23501
[8] Seal, H. L., The numerical calculation of U(w, t) the probability of non-ruin in an interval (0, t). Scandinavian Actuarial Journal, 121–139 (1974). · Zbl 0288.60088
[9] Seal, H. L., A note on the use of Laguerre polynomials in the inversion of Laplace transforms. Blätter der DGVM 12, 131–134 (1975). · Zbl 0313.65121 · doi:10.1007/BF02808584
[10] Taylor, G. C., On the radius of convergence of an inverted Taylor series with particular reference to the solution of characteristic equations. Scandinavian Actuarial Journal, 11–20 (1975). · Zbl 0316.60010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.