History of Life Contingency

The fundamental origin of life annuities is traceable back to the ancient Rome whereby a decree was introduced which permitted the inheritance of family inheritance by the first born sons. This decree was effected from 40 BC and the first born son was allowed a quarter of the inheritance altogether. This was a decree put forth by the Falcidian law of ancient Rome. The Falcidian law saw the gap which existed between the redeeming of the legacies at a reasonable market value and thus decided to create a valuation problem which made redeeming easier at the markets. Another group of people, jurist Ulpian, devised a table which was meant for determining the conversion of life annuities altogether. This Ulpian table was greatly concerned with life income maintenances. The tables also allowed for the trading of securities with definite cash flows which dependent upon the life contingencies. The aforementioned life annuities was established as a result of census which was defined as a form of investment carried out during the feudal era for the purpose of carrying out barter trade deals of the era. Although census was never used in the Roman law, other annuities were permitted and they included: fixed term annuities, perpetual and life annuities.  Amongst these investments, there were certain varieties of life annuities which were often issued by the states and municipalities. It should however be noted that with the introduction of these investments there were major setbacks formed which included the earliest forms of public debt which were issued by states and municipalities to wealthy individuals by way of forced loans. Examples of cities which practiced this form of investing were the Italian cities and cities which were located in the northern part of Europe. Municipalities in Holland and Flanders continued to practice the issuance of life and redeemable annuities which in turn increased public debts which were presented in terms of large stocks.

 With the booming of the investment lending business, there was created need for coming up with solutions for valuing life annuities. This life annuity involved three parties, the subscriber, the shareholder and the nominee. The earliest developments of life annuity valuations were instigated in Holland by de Witt who was the prime minister of the Dutch government. He proposed that the financing by life annuity be based upon the ages of the annuitants. This meant that different people were to be therefore allowed to finance the war with their life annuities which were based on their various ages.  Unlike the variations which were created by the numerous fixed term annuity problems which solved most of commercial arithmetic, the life annuity calculated the weight of the future cash flows according to the life span of the predetermined nominees. The assumption to this valuation proposal was that the nominee would survive long enough to service his life annuity. The major set back to this proposal was that it was cumbersome and complicated to deploy. It also faced political rejections during its debating in parliament.

With the tragic death of de Witt, emerged economists like de Moivre who took most of his time studying the practical problems which were to be used to determine the various prices of Life annuities. He eventually came up with a procedure which used probabilistic theories to evaluate and value life annuities. The assumptions which he used in developing the solution stipulated that the probabilities of life dropped off in an arithmetic progression. The limitation which befell de Moivre solution was the fact that it was so tedious to come up with figures for a single life annuity.