Life Contingencies

Life insurance and annuity valuation, survival models, and benefit reserves.

Key Concepts

• •Survival models: force of mortality, survival function, and curtate future lifetime
• •Life tables: q_x, p_x, l_x, d_x, and their relationships
• •Insurance present values: whole life, term, endowment, and deferred insurance
• •Annuity present values: whole life, temporary, deferred, and immediate/due distinctions
• •Net premiums: equivalence principle and loss-at-issue random variables
• •Gross premiums: expense loading, profit margins, and the gross premium equation
• •Benefit reserves: prospective and retrospective formulas, recursion relations
• •Multiple life models: joint life, last survivor, and contingent insurance
• •Multiple decrement models: competing risks and associated single decrement tables
• •Thiele differential equation: continuous reserve dynamics

Study Tips

• 1.Master actuarial notation (A_x, a_x, P_x, V_x) before attempting problems.
• 2.Draw timeline diagrams for every insurance and annuity problem.
• 3.Practice converting between continuous and discrete models.
• 4.Work recursion formula problems both forwards and backwards.
• 5.Understand the intuition behind reserves: why they increase then decrease.

Related Exam Resources