From conjecture to calculation ortality tables were often the work of clerics who wanted to discover the role and plans of a divine creator MITI CONJICTNDI In 1654, the French nobleman Chevalier grouped by age range, interest was shared de mere was vexed by uncertainties in his out and paid to subscribers annually en a nominee #需乱点:操 what the chances were of rolling a six in5 scriber s share in the annuity became certain sequence. The mathematicians oid, and the remaining subscribers Blaise Pascal and Pierre de Fermat used within the age range received an increased an old pyramid of numbers and eventually share of the interest. Many tontines were were able to prove that a mathematical fraudulent or badly undersubscribed probability could be determined and eventually were turned into simple This triggered a revolution in the development of probability theories It was only later in the 18th century that and mathematicians all over Europe life insurance was put on a healthier operated and applied their findings to calculate life expectancy. 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On this basis, the order behind the apparent randomness Welshman Richard Price later developed Blaise Pascal as a twelve year old boy Together of mortality a cost and accounting model. In 1774 with Pierre de fermat he late he calculated profitability in life insurance basis for probability calcul thich were surance was slow to adopt ti itable Life based on current to have a lasting impact on new science. Various forms of annuit and expected mortality, so that prevailed, resembling gambling more current state of the operations co than assurance. For some time so-called assessed more precisely. tontine schemes named after their creator Lorenzo Tonti, had enjoyed great From then on, life insurance no longer success, especially in Italy and France relied on speculation Subscribers could buy a share in a kind of life annuity based on the mortality of an appointed nominee With nominees Swiss Re A History of InsuranceSwiss Re A History of Insurance 9 From conjecture to calculation In 1654, the French nobleman Chevalier de Méré was vexed by uncertainties in his gambling pastime. He wanted to know what the chances were of rolling a six in a certain sequence. The mathematicians Blaise Pascal and Pierre de Fermat used an old pyramid of numbers and eventually were able to prove that a mathematical probability could be determined. This triggered a revolution in the development of probability theories and mathematicians all over Europe cooperated and applied their findings to calculate life expectancy. This attempt at predicting the future was in direct opposition to Church doctrine but, ironically, it was the Church whose mortality tables provided some of the input used in those early probability calculations. Mortality tables were often the work of clerics who wanted to discover the role and plans of a divine creator and prove the clear regularities and divine order behind the apparent randomness of mortality. Life insurance was slow to adopt the new science. Various forms of annuities prevailed, resembling gambling more than assurance. For some time so-called “tontine” schemes, named after their creator Lorenzo Tonti, had enjoyed great success, especially in Italy and France. Subscribers could buy a share in a kind of life annuity based on the mortality of an appointed nominee. With nominees grouped by age range, interest was shared out and paid to subscribers annually. When a nominee died, the associated subscriber’s share in the annuity became void, and the remaining subscribers within the age range received an increased share of the interest. Many tontines were fraudulent or badly undersubscribed and eventually were turned into simple life annuities. It was only later in the 18th century that life insurance was put on a healthier footing. James Dodson, a 45-year-old English mathematician, was refused insurance because of his advanced age. This annoyed him so much that he searched for a mathematical solution in order to form a more equitable base upon which to calculate premiums as a percentage of life expectancy. This principle was to be adopted by the English Equitable Life Assurance Society in 1766. On this basis, the Welshman Richard Price later developed a cost and accounting model. In 1774 he calculated profitability in life insurance for the Equitable Life based on current and expected mortality, so that the current state of the operations could be assessed more precisely. From then on, life insurance no longer relied on speculation. Mortality tables were often the work of clerics who wanted to discover the role and plans of a divine creator. Above: Pascal’s triangle was used by the Swiss mathematician Jacob Bernoulli who contributed the law of large numbers to actuarial science. This was to become the axiom from which life insurers could calculate expected losses. Opposite: Blaise Pascal as a twelve year old boy. Together with Pierre de Fermat he later developed the basis for probability calculations which were to have a lasting impact on life insurance