ACTUARY Actuarial Models Flashcards
5 cards from real Actuary Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 5 ACTUARY Actuarial Models flashcards as text
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?
Answer: 0.15
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?
Answer: $9,500
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?
Answer: $1,120
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?
Answer: 0.95
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?
Answer: $5,000
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