FREE ACTUARY Actuarial Models Questions and Answers

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The probability that a person aged 40 survives to age 50 is 0.85. What is the probability that the same person dies before age 50?

Correct! Wrong!

The probability of death is the complement of the survival probability: P(death before 50)=1−P(survival to 50)=1−0.85=0.15

An insurance company covers losses up to $10,000 per claim. If the probability distribution of losses is: P(X≤10,000)=0.7, P(X>10,000)=0.3, and the average claim for losses exceeding $10,000 is $15,000, what is the expected claim amount?

Correct! Wrong!

The expected claim amount is calculated as: E(X)=P(X≤10,000)⋅10,000+P(X>10,000)⋅15,000 E(X)=(0.7⋅10,000)+(0.3⋅15,000)=7,000+4,500=9,500

An insurance company observes that the average claim amount for a policyholder is $1,200, based on past experience. The population mean is $1,000 with a variance of $400. What is the Bayesian estimate of the claim amount if the weight of credibility (Z) is 0.6?

Correct! Wrong!

The Bayesian estimate is a weighted average of the policyholder's mean and the population mean: Bayesian Estimate=Z⋅Policyholder Mean+(1−Z)⋅Population Mean Bayesian Estimate=(0.6⋅1,200)+(0.4⋅1,000)=720+400=1,120

The hazard rate for a survival model is given by ℎ(𝑡)=0.02. What is the probability that an individual survives beyond time t=5?

Correct! Wrong!

The survival probability is related to the hazard rate through the cumulative hazard function: S(5)=e −0.1 ≈0.95

An insurance company models aggregate losses as the sum of 𝑁 independent claims, where 𝑁 follows a Poisson distribution with mean 𝜆=5, and each claim amount is $1,000. What is the expected aggregate loss?

Correct! Wrong!

E(Aggregate Loss)=E(N)⋅E(Claim Amount) Here, Here, E(N)=λ=5E(Claim Amount)=1,000: E(Aggregate Loss)=5⋅1,000=5,000

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