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Models (Characteristics of a good model (also think of VARIABLE CRISPS…

- - - - P(x,t) = l(x,t) k(x,t) a(x,t)
        P(x,t)= pension expenditure at start of year t for those aged x
        l(x,t)= population aged x at time t
        k(x,t)= proportion of the population aged x receiving pension at time t
        a(x,t) = average amount of pension for those aged x at time t
      - if flat rate benefit
        
        P(x,t)= l(x,t) k(x,t) B(x,t) X(t)
        B(x,t)= average proportion of full benefit rate for those aged x at time t
        X(t)= full benefit rate at time t
      - If assume patterns of expenditure are broadly continuous over the year, total projected annual pension expenditure in year t can be approximated by:
        
        0.5 Σ P(x,t) + 0.5 x Σ P(x,t+1)
    - - First necessary to calculate pension awards in each future year
      - these amounts are projected forward allowing for survival and future pension increases
      - P(x,t)= P(x-1, t-1) (1 + i(t-1)) l(x,t) / l(x-1,t-1)
        l(x,t_= population aged x at time t
        i(t-1)= pension increases from t-1 to t
- - - - prospective benefits funding method
- - - - Takes each future benefit payment and applies a discount factor to obtain a present value
    - - Simplifies the calculations
      - e.g. by valuing a pension for each member by multiplying it by an annuity and adding up for all members
    - - useful when the following are significant to the decision-making process:
        
        incidence of benefits/ contributions
        
        variance of level of benefits/ contributions
        
        covariances with asset proceeds