A rebirth of commutation functions in Excel

摘要

Commutation functions were born for simplifying the massive, complicated and burdensome calculations in life insurance mathematics; then, with the rapid development of modern technologies, the popularization of increasingly powerful computers has seemed to terminate the glorious age of commutation functions. However, this does not necessarily imply an end of the commutation functions; indeed, the fading commutation functions could find a new birth, according to the author, by using one-to-one correspondence method (i.e. the way to associate a notation of commutation functions with the name of a cell in Excel, such as D_(25) and D25). This essay first implements a general research on commutation functions; and then, based on an explicit analysis of the author's previous papers, expects to figure out the improvement of commutation functions in the application of life insurance mathematics; and finally, it discusses some problems which need to be further settled. Especially, construct the continuous and fraction-type commutation function tables and unified commutation function table in this paper for the first time. Simultaneously, three examples are proposed to run a further test to prove the simplicity of applying commutation functions to life insurance mathematics with the help of Excel.