LTAM Glossary

Key terms and definitions for Exam LTAM: Long-Term Actuarial Mathematics. Use this reference to review the most important concepts tested on the exam.

Force of Mortality
mu_x = -S'(x)/S(x), the instantaneous rate of death at age x. Analogous to the hazard rate in survival analysis. Higher values indicate greater mortality risk at that age.
Curtate Future Lifetime
K_x = floor(T_x), the integer number of complete years lived by (x) before death. Used in discrete life insurance and annuity formulas.
Whole Life Insurance
A life insurance policy that pays a benefit upon the death of the insured, whenever death occurs. The actuarial present value is A_x = sum of v^(k+1) * P(K_x = k) for k = 0, 1, 2, ...
Term Life Insurance
Life insurance that pays a benefit only if death occurs within n years. The actuarial present value is A_x:n (with 1 above the x). It equals A_x minus the deferred whole life value.
Endowment Insurance
A policy that pays a benefit at death if death occurs within n years, or a survival benefit at time n if the insured is still alive. Combines term insurance and a pure endowment.
Life Annuity-Due
A series of payments of 1 at the beginning of each year while the annuitant is alive. The actuarial present value is a-double-dot_x = sum of v^k * P(K_x >= k) for k = 0, 1, 2, ...
Net Premium
The premium calculated using the equivalence principle: the present value of premiums equals the present value of benefits. It does not include expenses or profit margin.
Net Premium Reserve
The difference between the present value of future benefits and the present value of future net premiums, evaluated at time t. It represents the insurer s liability for an in-force policy.
Equivalence Principle
The principle that the expected present value of premiums equals the expected present value of benefits at the time of policy issue. Used to determine net premiums and is the foundation of reserve calculations.
Multiple-Decrement Model
A model where an individual can leave the active state through multiple causes (death, disability, withdrawal, etc.). Each cause has its own force of decrement, and the total force is the sum of all individual forces.
Joint-Life Status
A status that terminates at the first death among a group of lives. For two lives x and y, the joint-life survival probability is t_p_xy = t_p_x * t_p_y (assuming independence).
Profit Testing
A technique for projecting the expected cash flows (premiums, benefits, expenses, reserves) of an insurance product year by year. Used to assess profitability and set premium levels.