Life Insurance A 35 -year-old woman purchases a 100,000 term life insurance policy

step 1 Hi, this is problem 18 of chapter 5, section 2. In this problem, a woman is paying $360 per year

Life Insurance A 35 -year-old woman purchases a ...

$$ \begin{array}{l}{\text { Life Insurance A } 35 \text { -year-old woman purchases a }} \\ {\$ 100,000 \text { term life insurance policy for an annual pay- }} \\ {\text { ment of } \$ 360 . \text { Based on a period life table for the U.S. }} \\ {\text { government, the probability that she will survive the }} \\ {\text { year is } 0.999057 . \text { Find the expected value of the policy }} \\ {\text { for the insurance company. }}\end{array} $$

$$
\begin{array}{l}{\text { Life Insurance A } 35 \text { -year-old woman purchases a }} \\ {\$ 100,000 \text { term life insurance policy for an annual pay- }} \\ {\text { ment of } \$ 360 . \text { Based on a period life table for the U.S. }} \\ {\text { government, the probability that she will survive the }} \\ {\text { year is } 0.999057 . \text { Find the expected value of the policy }} \\ {\text { for the insurance company. }}\end{array}
$$

Key Concepts

Survival Analysis

Survival analysis is a statistical approach used to analyze the expected duration until one or more events occur, such as death or failure. In life insurance, it involves assessing the likelihood that an individual survives a given period based on life tables and other demographic data, which is crucial for setting premiums and predicting future liabilities.

Life Insurance Valuation

Life insurance valuation involves balancing the premiums received from policyholders against the potential benefits paid out in the event of claims. Actuaries use survival probabilities, expected value calculations, and other risk evaluation techniques to ensure that premiums are set at levels that adequately cover potential losses while also providing a profit margin for the insurer.

Expected Value

Expected value is the weighted average of all possible outcomes where each outcome is multiplied by its probability. In the context of risk assessments and insurance, this concept enables actuaries and financial analysts to determine the average gain or loss associated with an uncertain event by summing all products of possible gains (or losses) and their respective likelihoods.

Probability Theory

Probability theory provides the mathematical framework for quantifying uncertainty and risk. It involves assigning probabilities to various events—such as survival or death in the case of life insurance—and is used to model and analyze scenarios where outcomes are uncertain, forming the basis for computing expected values.

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