Johan de Witt - The first calculation on the valuation of life annuities MacTutor Index

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## Abstract

This paper is treating the life and work of Dutch 17th century statesman Johan de Witt. Looking at the historical background, the development of state finances, and de Witt's political career enables the reader to assess the circumstances in which the paper in question, the "Waerdye van Lijf-renten naer proportie van Los-renten", was written. De Witt presented it shortly before the third Anglo-Dutch War in 1671 as a proposal to raise a war budget through the financial instrument of life annuities, instead of alternatives. Life annuities represented a contract between the seller - usually the state - and the annuitant, who received a periodical compensation after payment of a lump sum. This payment was only received as long as the "life" on which the contract was written, usually a young child, was proven to be alive. De Witt was the first to attempt a pricing of annuities on mathematical grounds, and used his mathematical education as well as recently developed statistical concepts to calculate the expected value of an annuity. He used an estimation of mortality rates to account for a non- linear life expectancy throughout life, and arrives at a value of 16 mio guilders - 4 mio more than they were trading at the time. Close attention reveals that de Witt in fact miscalculated, which leads to the speculation that he deliberately manipulated his valuation to arrive at a convincing result. Regardless of the error, the treatise presents an impressive piece of mathematical work, that can be put into perspective by looking at work of other mathematicians in the field of insurance statistics in the following centuries.

My reflection arrives at the conclusion that the "Waerdye" not only instructs on statistical content of some value. Importantly, it reminds any reader of mathematical work to keep context and purpose in mind to be able to critically reflect, and register manipulations as the one we likely observe in de Witt's treatise.

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Livia Daxenberger May 2017