Modified Reserves: Full Preliminary Term Method

Why Modified Reserves

Net level premium reserves assume level expense loading, but actual expenses are heavily front-loaded (first-year commissions, underwriting costs). This creates a "new business strain" where first-year reserves are higher than the asset share, requiring surplus. Modified reserve methods adjust first-year premiums downward and renewal premiums upward to better match the expense pattern while still satisfying regulatory requirements for minimum reserves.

Full Preliminary Term (FPT) Method

The FPT method treats the first year as one-year term insurance. The first-year modified premium alpha equals the cost of one-year term: alpha = v*q_x. Renewal premiums beta are set so that the total present value of premiums equals the APV of benefits: beta = (A_x minus A_{x:1}^1) / (a-ddot_x minus a-ddot_{x:1}) = A_{x+1} / a-ddot_{x+1} = P_{x+1}. The FPT reserve at duration t >= 1 is t-1_V_{x+1}, equivalent to treating the policy as if it were issued one year later at the net premium for age x+1. Exam LTAM tests FPT and other modification methods.