ADONGO’S RISK THEOREM

Social Security Schemes by their very nature require risk assessments and analysis to ascertain the viability and sustainability of the schemes into the future. SSNIT risk assessments are reviewed every three years. These assessments are based on a set of assumptions that are reasonable to the actuaries. The SSNIT risk assessments assumptions are categorized into three.

1) Population distribution of deaths and life expectancy data.

2) General economic growth data.

3) The operational and administrative experience of SSNIT over the years.

1POPULATION DISTRIBUTION OF DEATHS

One measure of risk in life insurance is the standard deviation of the possible outcomes in each age group. If we look at a particular individual in each age group, we see in possible outcomes, each with a specific economic by purchasing an insurance policy company in exchange for a fixed premium. We might conclude that if an insurer sells n policies to n deaths, it assumes the total risk of n deaths.

In real life, the risk assumed by the insurer is small in total in each age group than the sum of the risk associated with each individual policyholder in each age group. The results are shown in my theorem below.

THEOREM: Let dx₁, dx₂,……,dx_n be independent random variables such that each d_xi has an expected death  d^*_xi  and variance of Z²_x. Let S_n =dx₁+dx₂+……+dx_n. Then E(Sn)=n_*E(dx_i)=nd^*_xi ,

    Z_x=(d_x-d^*_x)/√(d^*_x(1-q*x) 
   d^*_xi=e^2xiqxi  for each i=1.2,3,….

The standard deviation of  S_n is  √n*Z_x,  which is less than  nZ_x, the sum of the standard Deviation for each policy in each age group. Furthermore, the coefficient of variation, which is the ratio of the standard deviation to the expected death, is

C_f=Z_x/√n*d*_x

C_f==(dx-d*x)/ √[d*x(1-q*_x)*n]*d*_x

The coefficient of variability’s between positive distributions with different expected values in each group. So, given n independent policyholders in each age group, as n becomes very large, the insurer’s risk, as n measured by the coefficient of variation is aimed at assessing risk of life insurance to provide your family with additional economic security should you die unexpectedly. Generally, life insurance provides for a fixed benefit at death.

REFERENCE

*Adongo, Bill (Me): Diary(Weblog), “Adongo Minimum Method Of Uncertainty”