AWAY

Apologies that I'm unable to post today. I'm away at a conference and will post tomorrow. Thanks a lot.

SOA EXAM P SAMPLE QUESTION 7 - SET THEORY

Question:
An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto policy and a homeowners policy will renew at least one of those policies next year.

Company records show that 65% of policyholders have an auto policy, 50% of policyholders have a homeowners policy, and 15% of policyholders have both an auto policy and a homeowners policy.
Using the company’s estimates, calculate the percentage of policyholders that will renew at least one policy next year.

Solution:

SOA EXAM P SAMPLE QUESTION 131 - CONDITIONAL PROBABILITY

Deductible Question SOA Exam P Sample Question 51

INCREASING ANNUITIES QUESTION: SOA SAMPLE QUETION 31

Question:
An insurance company has an obligation to pay the medical costs for a claimant. Annual claim costs today are 5000, and medical inflation is expected to be 7% per year. The claimant will receive 20 payments.Claim payments are made at yearly intervals, with the first claim payment to be made one year from today.
Calculate the present value of the obligation using an annual effective interest rate of 5%.

Solution:

VARIANCE PROBLEM (Marcel B. Finan; Sample Exam 1, Question 31)

Question: An insurance policy pays a total medical benefit consisting of two parts for each claim. Let X represent the part of the benefit that is paid to the surgeon, and let Y represent the part that is paid to the hospital. The variance of X is 5000, the variance of Y is 10,000, and the variance of the total benefit, X + Y; is 17,000. Due to increasing medical costs, the company that issues the policy decides to increase X by a flat amount of 100 per claim and to increase Y by 10% per claim.
Calculate the variance of the total benefit after these revisions have been made.

Solution:

RAINMAKER PROBLEM

Question: Ade assigns scores to meteorologists (because he has nothing better to do) in the following manner: if a meteorologist says there is a probability p of rain tomorrow, then they get the score 1 − (1 − p)^2 , if it rains tomorrow and 1 − p^2 , if it doesn’t rain tomorrow.
This way, the score for a wrong prediction is very low if the prediction was confident (p close to 0 or 1), but not too punishing if the prediction was uncertain (p close to 1/2). Suppose I am a meteorologist who somehow always knows the correct probability of rain (I'm a rainmaker). I know there is a chance of 3/10 of rain tomorrow. What should I tell Ade the probability is, in order to maximize my expected score from him?