MATRIX ANALYSIS OF THE CASH FLOWS AND RESERVES OF A LIFE OFFICE

Matrix projection methods have been used by demographers to prove a number of powerful general theorems concerning population growth and development. The methods have also been applied to the study of graded social systems and to problems of manpower planning. The policy-holders of a life office and the members of a superannuation fund belong to graded systems with age as the important hierarchical variable. The abovementioned methods can therefore be used to study the growth and development of the membership of these institutions.
Recent articles by Sherris (1977), and Pollard and Sherris (1979a, 1979b) have shown that matrix analysis is also very useful for projecting the cash flows and reserves of life assurance companies and superannuation funds.
In this paper the use of these methods is illustrated by the projection of the reserves of a life office writing whole-life assurance contracts. We find that as the fund matures, it grows exponentially.