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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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The life and work of Olof Thorin (1912–2004); pp. 18–25

(Full article in PDF format) doi: 10.3176/proc.2008.1.02


Authors

Lennart Bondesson, Jan Grandell, Jaak Peetre

Abstract

This paper reviews Olof Thorin’s contributions to mathematical analysis, actuarial mathematics, and probability theory, though in reversed order. In probability theory he is known for his path-breaking work on infinite divisibility. In actuarial mathematics he contributed significantly to the ruin problem. However, his international fame very much relies on his work in mathematical analysis and his share in the Riesz–Thorin theorem. Data about his life and some personal recollections are also given.

Keywords

actuarial mathematics, infinite divisibility, interpolation spaces, Riesz–Thorin theorem, ruin problem.

References

  1. Feller , W. An Introduction to Probability Theory and Its Applications , Vol. II. Wiley , New York , 1966.

  2. Steutel , F. W. Some recent results in infinite divisibility. Stochastic Processes Appl. , 1973 , 1 , 125–143.
doi:10.1016/0304-4149(73)90008-2

  3. Thorin , O. On the infinite divisibility of the lognormal distribution. Scand. Actuar. J. , 1977 , 1977 , 121–148.

  4. Thorin , O. On the infinite divisibility of the Pareto distribution. Scand. Actuar. J. , 1977 , 1977 , 31–40.

  5. Thorin , O. Proof of a conjecture of L. Bondesson concerning infinite divisibility of powers of a gamma variable. Scand. Actuar. J. , 1978 , 1978 , 151–164.

  6. Thorin , O. An extension of the notion of a generalized G-convolution. Scand. Actuar. J. , 1978 , 1978 , 141–149.

  7. Bondesson , L. Generalized Gamma Convolutions and Related Classes of Distributions and Densities. Lecture Notes in Statistics , No.~76. Springer-Verlag , New York , 1992.

  8. Steutel , F. W. and van Harn , K. Infinite Divisibility of Probability Distributions on the Real Line. Marcel Dekker , New York , 2004.

  9. Barndorff-Nielsen , O. E. , Maejima , M. and Sato , K.-I. Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations. Bernoulli , 2006 , 12 , 1–33.

10. Lundberg , F. Approximerad Framställning av Sannolikhetsfunktionen. II. Återförsäkring av Kollektivrisker (Approximate representation of the probability function. II. Reinsurance of collective risks). Almqvist & Wiksell , Uppsala , 1903 (in Swedish).

11. Lundberg , F. Försäkringsteknisk Riskutjämning. I: Teori. II: Statistik (Insurance technical smoothing of risks). F. Englunds Boktryckeri AB , Stockholm , 1926 (and 1928) (in Swedish).

12. Cramér , H. On the Mathematical Theory of Risk. Skandia Jubilee Volume , Stockholm , 1930. Reprinted in Harald Cramér: Collected Works , Vol. I (Martin-Löf , A. , ed.). Springer-Verlag , Berlin , 1994 , 601–678.

13. Cramér , H. Collective Risk Theory. Skandia Jubilee Volume , Stockholm , 1955. Reprinted in Harald Cramér: Collected Works , Vol. II (Martin-Löf , A. , ed.). Springer-Verlag , Berlin , 1994 , 1028–1115.

14. Thorin , O. An identity in the collective risk theory with some applications. Skand. Aktuarietidskr. , 1968 , 1968 , 26–44.

15. Sparre-Andersen , E. On the collective theory of risk in the case of contagion between the claims. In Transactions of the 15th International Congress of Actuaries , New York , II. 1957 , 219–229.

16. Thorin , O. Probabilities of ruin. Scand. Actuar. J. , 1982 , 1982 , 65–102.

17. Thorin , O. and Wikstad , N. Calculation of ruin probabilities when the claim distribution is lognormal. Astin Bull. , 1977 , 9 , 231–246.

18. Peetre , J. On the development of interpolation – Instead of a history three letters. Edited and/or translated by Jaak Peetre. In Function Spaces , Interpolation Theory and Related Topics (Cwikel , M. et al. , eds). Walter de Gruyter , Berlin , 2002 , 39–48.

19. Peetre , J. Marcel Riesz in Lund. In Function Spaces and Applications (Cwikel , M. et al. , eds). Lecture Notes in Mathematics , 1302 , Springer-Verlag , Berlin , 1988 , 1–10.

20. Thorin , O. An extension of the convexity theorem of M. Riesz. Kungl. Fysiogr. Sällsk. Lund Förh. , 1939 , 8 , No. 14.

21. Thorin , O. Convexity theorems generalizing those of M. Riesz and Hadamard with some applications. Medd. Lunds Univ. Mat. Sem. , 1948 , 9 , 1–58.

22. Peetre , J. Interpolation functors and Banach couples. In Actes du congrès international des mathématiciens , 1970 , Nice , France , t. 2. Gauthiers-Villars , Paris , 1971 , 373–378.

23. Bergh , J. and Löfström , J. Interpolation Spaces. An Introduction. Grundlehren der mathematischen Wissenschaften , 223. Springer-Verlag , Berlin , 1976.

24. Riesz , M. Sur les maxima des formes bilinéaires et sur les fonctionelles linéaires. Acta Math. , 1927 , 49 , 465–497.
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25. Littlewood , J. E. A Mathematician’s Miscellany. Methuen , London , 1953.

26. Marcinkiewicz , J. Sur l’interpolation d’opérations. C. R. Acad. Sci. , Paris , 1939 , 208 , 1272–1273.
 
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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December