Biography of August Zillmer
August Zillmer (18311893) was a German speaking life insurance actuary. Zillmer was an officer/director of several life insurance firms. Zilllmer was the author of the first comprehensive actuarial mathematics text since Tetens text almost a century earlier. He brought about the founding of the Institute of Actuarial Science at Berlin in 1868. As head of the Institute in 1883 he oversaw the publication of the first multi-company mortality study on the continent. He is best known for the development of the Zillmer Method of valuing life insurance reserves. Zillmer also published a number of valuable professional articles in the Insurance Annual (Assecuranzjahrbuch).
August Zillmer was born on January 23, 1831, in TreptowontheRega, Prussia. His father was a master mason. After completion of his studies at the city school of Vaterstadt in March of 1847, he enrolled in the high school at the Old Cloister in Berlin during the summer of 1847. He passed his final exams at Easter time in 1851. Then he studied mathematics and science at the University of Berlin. After earning his doctoral degree in 1858 from the University of Rostock on the basis of an unpublished dissertation, he became the actuary for the Germania Life Insurance Company in Stettin, Prussia. In 1867, he moved to Berlin as the second director of the newly established Northstar Life Insurance Company. He stayed there until 1876 when he went to Elberfeld as director of the Fatherland's Life Insurance Company. Because of the death of his youngest child, a daughter, he took a dislike to life in the country in Elberfeld. Therefore in 1882, he returned to Berlin. In 1883, his wife died. Zillmer died in Berlin on February 22, 1893, after a siege of asthma lasting several months.
Zillmer is credited for the first systematic and self-contained German textbook of actuarial mathematics since the text by Johan Nicolaus Tetens in 1785-1786. The first edition of The Mathematical Theory of Life Insurance and Annuities (Die mathematischen Rechnungen bei Lebens und Rentenversicherungen) was published in Berlin in 1861; the second edition was published in 1887. Being compared to Tetens (17361807) puts Zillmer in very select company. Tetens was a mathematician, philosopher, royal counselor, and actuary. As an actuary he was responsible for the development of the life commutation functions (Dx, etc.) and the columnar method of calculating life insurance values. Tetens described a life insurance contract as a game with a random outcome and calculated the expected value of that game. Zillmer's name is associated with the Zillmer method of calculating modified life insurance reserves. Modified reserves allow insurance companies to reduce their liabilities, reserves, to take into account the expense of issuing life insurance contracts while assuring that adequate provision is made for policyholder security. The Zillmer Method allowed for issue expenses of as much as 1.25% of the face amount of insurance. The first year's net premium and terminal reserve were to be correspondingly reduced. In subsequent years, the net premium must be larger to allow for the amortization of the issue expense over the premium payment period (or some shorter period). Eventually, the Zillmer reserve and the net premium reserve will coincide. Zillmer first published his method in a monograph Contributions to the Theory of Life Insurance Reserves (Beitrage zur Theorie der Prámienreserve) in Stettin in 1863. The Zillmer Method did not become the standard valuation technique in Germany for some time. Just as established American companies fought against preliminary term valuation, established German companies fought against the Zillmer method. The net premium reserve method was a significant barrier to entry into the life insurance industry. The established German companies were able to safeguard their markets and their profits almost into the 20th century. Prior to the Zillmer Method, German companies used net premium reserves or select-and-ultimate reserves. By 1909, the Insurance Dictionary (VersicherungsLexicon, Alfred Manes) documents that the Zillmer Method was part of Imperial German Law. Zillmer's third major publication was a mortality study. Zillmer was the head of the commission which published German Mortality Table from the Experience of Twenty-three Life Insurance Companies (Deutsche Sterblichkeitstafeln aus den Erfahrungen von dreiundzwanzig LebensVersicherungs Gesellschaften) in Berlin in 1883. The report of the mortality study was unique in that it included: 1) the complete methodology of the study including form letters, questionnaires, data forms, and worksheets. 2) separate mortality for men and women. 3) separate mortality for medically underwritten and nonmedical business. 4) separate mortality for industrial and ordinary insurance. 5) juvenile mortality. 6) select mortality. 7) raw data which allowed users to perform their own graduation and analysis of the mortality. The text of the study is a veritable tome of some 880 pages. At the turn of the century, the basic table in this study (M & F I) was the actuarial basis for about 75% of the medically underwritten, ordinary insurance written by the German companies. Wilhelm Lazarus (18251890) collaborated with Zillmer in the construction of the mortality table cited above. Lazarus, in fact, wrote the summary "Report to the Commission on the Implementation of the Preparation for the Creation of a Mortality Table from the Experience of German Life Insurance Associations" which introduces the mortality study. The literature gives Lazarus a substantial share of the credit for the design of the study and graduation of the mortality data according to GompertzMakeham Law of Mortality. The design of the study included the use of census cards, a practice subsequently adopted by English speaking actuaries. Zillmer also relied on Lazarus' critique of other modified reserving methods in Contributions. Zillmer cites the same Lazarus paper twice in Contributions; Lazarus is the only actuary cited explicitly by Zillmer in that text.
Considerations Related to Simple Interest Calculation with Special Application to the Oettinger Proof (Betrachtungen uber die einfache Zinsrechnung, mit besonder Rucksicht auf den Oettingerschen Bewies, etc.) (Stettin, 1864)
August Zillmer made a substantial contribution to actuarial science, but his work is not well-known to English speaking actuaries. His work may have been the victim of the NIH (not invented here) syndrome or misguided English nationalism. In Contributions, Zillmer is quite critical of the valuation methods used in the balance sheets and income statements of British insurance companies. Zillmer was a Victorian version of Ralph Nader. Before the English had time to reform their own industry, they were at war with Imperial Germany. Praising the contributions of German actuaries would not have seemed very important. Zillmer may have been his own worst enemy in that his critique of the accounting practices of the English companies seems unnecessarily nationalistic. Current trends in the international insurance business make it likely that Zillmer will come into his own. The Zillmer Method is sanctioned in the reserve regulation of Japan and the European Economic Community. The rapid growth of the life insurance industry in these areas will prompt a re- evaluation of the work of Zillmer.