Profit Testing for Life Insurance Products

Profit Vector and Profit Signature

Profit testing projects a policy's expected cash flows year by year. The profit vector Pr_t is the expected profit emerging in year t per policy in force at the start of year t. It includes premium income, investment income on reserves, less benefit payments, expense outgo, and the increase in reserves. The profit signature pi_t = Pr_t * product of (1 minus q_{x+k-1}^(tau)) for k=1 to t-1 converts per-in-force profits to per-policy-issued profits by multiplying by the probability of surviving to the start of year t in the multiple decrement environment.

Profitability Measures

The net present value (NPV) discounts the profit signature at the risk discount rate: NPV = sum of pi_t * v_r^t. The internal rate of return (IRR) is the rate making NPV equal to zero. The discounted payback period is the earliest time the cumulative discounted profit signature turns positive. Exam LTAM problems require constructing profit test tables, calculating each component, and evaluating profitability measures to assess product viability or determine the premium that achieves a target profit level.