Term Life Insurance: Pricing and Reserving for Exam LTAM

Term Insurance APV

An n-year term insurance pays a benefit only if death occurs within n years. The continuous APV is A-bar_{x:n}^1 = integral from 0 to n of v^t * t_p_x * mu_{x+t} dt. The discrete APV is A_{x:n}^1 = sum from k=0 to n-1 of v^{k+1} * k_p_x * q_{x+k}. The relationship A_x = A_{x:n}^1 + n_E_x * A_{x+n} decomposes whole life into term plus deferred whole life, where n_E_x = v^n * n_p_x is the pure endowment factor.

Term Insurance Reserves

The net premium for n-year term insurance is P_{x:n}^1 = A_{x:n}^1 / a-ddot_{x:n}, where a-ddot_{x:n} is the temporary life annuity-due. The prospective reserve at time t (for t < n) is t_V = A_{x+t:n-t}^1 minus P * a-ddot_{x+t:n-t}. Term reserves are typically small and decrease toward zero at duration n. Exam LTAM problems may involve calculating reserves at specific durations, comparing prospective and retrospective reserve formulas, and understanding how mortality improvements affect term insurance pricing.