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Prof. Dr. Hans Bühlmann

Prof. Dr. Hans Bühlmann

Postal Address:
Department of Mathematics
ETH Zurich
HG J58
8092 Zurich
Switzerland
Private Address:
Nidelbadstrasse 22
CH-8803 Rüschlikon
Switzerland
Phone: +41-44-724 10 84

Go down to: Curriculum vitae


List of Publications:

  1. Änderungen in der Grundgesamtheit der Betriebsunfallkosten (with W. Hartmann), Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1956
  2. Sur l'indépendence asymptotique des variables aléatoires liées, Comptes Rendus des Séances de l'Académie des Sciences, Paris, 1957
  3. Le problème limite central pour les variables aléatoires échangeables liées, Comptes Rendus des Séances de l'Académie des Sciences, Paris, 1958
  4. Die beste erwartungstreue lineare Schätzfunktion der Übersterblichkeit, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1959
  5. Austauschbare stochastische Variablen und ihre Grenzwertsätze, Dissertation, University of California Press, Berkeley and Los Angeles, 1960
  6. Über das Testen von Sterblichkeitshypothesen über anomale Risiken, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1961
  7. Pairwise comparison and ranking in tournaments (with P. Huber), Annals of Mathematical Statistics, USA, 1963
  8. L2-Martingales and Orthogonal Decomposition, Habilitation, Zeitschrift für Wahrscheinlichkeitstheorie, Springer, Deutschland, 1963
  9. A distribution free method for general risk problems, ASTIN Bulletin, Zürich and London, 1964
  10. Optimale Prämienstufensysteme, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1964
  11. Die Geburtsstunde der mathematischen Statistik, Antrittsrede, Vierteljahresschrift der Naturforschenden Gesellschaft in Zürich, 1964
  12. Die Risikoaversion als Interpretation und Konstruktionsbasis der Utilitätskurve, Metrika, Wien und Würzburg, 1965
  13. Experience rating and credibility, ASTIN Bulletin, Amsterdam and London, 1967
  14. Kollektive Risikotheorien, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1967
  15. Einführung in die Theorie und Praxis der Entscheidung bei Unsicherheit (with H. Löffel and E. Nievergelt), Lecture Notes in Operations Research, Springer, Berlin, Heidelberg, New York, 1967
  16. Marktverhalten unter Risiko - das Deckungsmonopol, 18. Internationaler Kongress der Versicherungsmathematiker, München, 1968.
  17. Individual, cooperative and competitive pricing of risks, Conference on Risk and Uncertainty IEA Smolenice, Czechoslovakia, 1969
  18. Note on the collective theory of risk, Skandinavisk Aktuarietidskrift, 1969
  19. Glaubwürdigkeit für Schadensätze (with E. Straub), Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1970
  20. Mathematical Methods in Risk Theory, Grundlehrenband 172, Springer-Verlag, Heidelberg, 1970
  21. Credibility procedures, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 1979
  22. On a transformation of the weighted compound Poisson process (with R. Buzzi), ASTIN Bulletin, Amsterdam and London, 1971
  23. Was ist mathematische Ökonomie?, Schweizer Zeitschrift für Volkswirtschaft und Statistik, 1971
  24. Der proportionale Rückversicherungsmarkt, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1971
  25. Ruinwahrscheinlichkeit bei erfahrungstarifiertem Portfeuille, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1972
  26. Decisioni applicate al processo aleatorio del rischio, Giornale dell'Istituto Italiano degli Attuari, Roma, 1972
  27. A comparison of three credibility formulae using multidimensional techniques, ASTIN Bulletin, Amsterdam and London, 1974
  28. The mincing machine revisited, ASTIN Bulletin, Amsterdam and London, 1975
  29. Entscheidungs- und Spietheorie (with H. Löffel and E. Nievergelt), Hochschultexte, Springer-Verlag, Berlin, Heidelberg, New York, 1975
  30. Il Problema di Pieni di Conservazione, Estratto dal Quaderno no. 29 dell'I.S.A., Trieste, 1975
  31. Minimax credibility, Scandinavian Actuarial Journal, 1976
  32. A probabilistic approach to long term insurance, International Congress of Actuaries, Tokyo, 1976
  33. Some inequalities for stop-loss premiums (with B. Gagliardi, H.U. Gerber, E. Straub), ASTIN Bulletin, 1977
  34. General jump process and time change - or, how to define stochastic operational time (with H.U. Gerber), Scandinavian Actuarial Journal, 1978
  35. Risk bearing and the insurance market (with H.U. Gerber), ASTIN Bulletin, 1978
  36. Versicherungsstatistik, Handwörterbuch der Wirtschaftswissenschaft, Vandenhoeck & Ruprecht, Göttingen and Zürich, pp. 326-333, 1979
  37. Unicity of Fair Pareto Optimal Risk Exchanges (with W.S. Jewell), Report ORC University of California, Berkeley, 1979
  38. Optimal risk exchanges (with W.S. Jewell), ASTIN Bulletin, 1979
  39. An economic premium principle, ASTIN Bulletin, 1980
  40. Claims reserves in casualty insurance based on a probability model (with R. Schnieper and E. Straub), Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1980
  41. Numerische Methoden zur Berechnung der Gesamtschadenverteilung, Mannheimer Vorträge zur Versicherungswissenschaft, Nr. 20, Institut für Versicherungswissenschaft der Universität Mannheim, 1981
  42. Excess claims and data trimming in the context of credibility rating procedures (with A. Gisler and W.S. Jewell), Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1982
  43. The general economic premium principle, ASTIN Bulletin, 1984
  44. Numerical evaluation of the compound Poisson distribution: recursion or fast Fourier transform?, Scandinavian Actuarial Journal, 1984
  45. Premium calculation from top down, ASTIN Bulletin, 1985
  46. Hierarchical credibility revisited (with W.S. Jewell), Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Bern, 1987
  47. Entwicklungstendenzen in der Risikotheorie, Jahresbericht der Deutschen Mathematikervereinigung, vol. 90, 1988
  48. Tendencies of development in risk theory, Proceedings of 1989 Centennial Celebration of the Society of Actuaries, Schaumburg, Illinois, 1989
  49. The Actuary, Insurance: Mathematics and Economics, Amsterdam, 1992
  50. Stochastic discounting, Insurance: Mathematics and Economics, Amsterdam, 1992
  51. La théorie du risque, son origine et ses tendances, Bulletin de l'Institut des Actuaires Français, no. spécial Centannaire, 1992
  52. Attualizzazione Stocastica, in: Un Corso sul Controllo del Rischio di Tasso di Interesse, eds.:Castellani, de Felice, Moriconi, Mottura, Società Editrice il Mulino, Bologna, 1993
  53. Continuous and discrete models in finance, in particular for stochastic interest rates, Rivista di Matematica per le Scienze Economiche e Sociali, 1994
  54. Über die Finanzierung der Rentenversicherung. Festschrift zum 60. Geburtstag von Karl-Heinz Wolff, Orac Verlag, Wien, 1994
  55. Life Insurance with Stochastic Interest Rates, in: Financial Risk in Insurance, ed.: G. Ottaviani, Springer-Verlag, Berlin, Heidelberg, New York, pp. 1-14, 1995
  56. Collective risk theory for assets, North American Actuarial Journal, 1997
  57. Credibility in the regression case revisited (A late tribute to Charles A. Hachemeister), with A. Gisler, ASTIN Bulletin, 1997
  58. The Actuary: The Role and Limitations of the Profession since the mid-19th Century, 1997
  59. No-arbitrage, change of measure and conditional Esscher transforms. CWI Quaterly, Amsterdam, 1997 (with F. Delbaen, P. Embrechts and A. Shiryaev)
    DVI (93 kB), PDF (215 kB), Compressed Postscript (206 kB), Postscript (636 kB)
  60. Fundamental theorem of asset-pricing, Esscher transforms and change of measure in the finite horizon, discrete multiperiod model. ASTIN Bulletin, 1998 (with F. Delbaen, P. Embrechts and A. Shiryaev)
    DVI (55 kB), PDF (168 kB), Compressed Postscript (182 kB), Postscript (492 kB)
  61. Mathematische Paradigmen in der Finanzwirtschaft (Abschiedsvorlesung ETH) Elemente der Mathematik 53, Birkhäuser, Basel 1998
  62. Selection of Credibility Regression Models (with P. Bühlmann) ASTIN Bulletin, 1999
  63. On the Prudence of the Actuary and the Courage of the Gambler (Entrepreneur) Giornale Istituto Italiano Attuari vol. LXV, Roma 2002
  64. New Math for Life Actuaries. Editorial ASTIN Bulletin, vol. 32(2), 2002
  65. A Discrete Time Benchmark Approach for Finance and Insurance. ASTIN Bulletin vol. 33(2), 2002 (with E. Platen)
  66. Multidimensional Valuation of Life Insurance Policies and Fair Value (with G. Baumgartner and M. Koller) Mitteilungen SAV I, 2004
  67. Multidimensional valuation. Finance, vol. 25, 15-29, 2004 PDF
  68. On Teaching Actuarial Science. Guest Editorial. British Actuarial Journal, vol. 9, Part III, No. 42, 491-492, 2003
  69. A Course in Credibility Theory and its Applications, Springer, Berlin, Heidelberg, 2005 (with A. Gisler)
  70. The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy revisited). ASTIN Bulletin, 36(2), 521-542, 2006 (with M. Buchwalder, M. Merz and M.V. Wüthrich)
  71. Valuation Portfolio in Non-Life Insurance. Scandinavian Actuarial Journal, 2007/2, 108-125 (with M. Buchwalder, M. Merz and M.V. Wüthrich)
  72. Estimation of Unallocated Loss Adjustment Expenses. Bulletin SAA, 2006/1, 43-53 (with M. Buchwalder, M. Merz and M.V. Wüthrich)
  73. The Valuation Portfolio. Bulletin SAA, 2007/1, 69-84 (with M. Merz)
  74. Market-Consistent Actuarial Valuation, EAA Lecture Notes, Springer Berlin, Heidelberg, 2008 (with M.V. Wüthrich and H. Furrer)
  75. A "Toy Model" for Operational Risk Quantification using Credibility Theory. Operational Risk, 2(1), 108-125, 2007 (with P. Shevchenko and M.V. Wüthrich)
  76. Bounds on the Estimation Error in the Chain Ladder Method. Scandinavian Actuarial Journal, 2008/4, 283-300 (with M. Merz and M.V. Wüthrich)
  77. Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result. ASTIN Bulletin, 39(1), 275-306, 2009 (with M. De Felice, A. Gisler, F. Moriconi and M.V. Wüthrich)
  78. The One Year Runoff Uncertainty for Discounted Claims Reserves. Giornale Istituto Italiano Attuari, Vol. LXXI, 1-37, 2008 (with M.V. Wüthrich)
  79. The One-Year Risk in Life Insurance with an Application to Pension Insurance. Festschrift für Dr. Peter Kunz, Brain Mappy Verlag, 2010 (with Olivier Deprez)


Curriculum Vitae:

Born 30 January 1930 in Chur (Switzerland), Swiss Citizen
Married, three children, six grandchildren

1. Education

University of Zürich venia legendi 1963
ETH Zürich Ph.D. 1959
ETH Zürich Diploma in Mathematics 1955

2. Employment

ETH Zürich Emeritus since 1997
ETH Zürich Full Professor of Mathematics 1966-1997
ETH Zürich President 1987-1990
ETH Zürich and Lausanne Vice-President of the Board 1987-1990
ETH Zürich Dean of the Faculty 1986-1987
ETH Zürich Chairman of the Department 1981-1985
Swiss Reinsurance Company Nonlife Actuary 1963-1966
University of California, Berkeley Visiting Assistant Professor 1961-1963
Swiss Reinsurance Company Actuary 1958-1961

Visiting Professor at the 3. Honours
Honorary President of Honorary Member of the Corresponding Member of the 4. Professional Activities
4.1 Past editorial duties 4.2 Past professional duties
4.3 Ph.D. students
Last revision: 25 October 2012