This section of sample problems and solutions is a part of The Actuary’s Free Study Guide for Exam 5, authored by Mr. Stolyarov. This is Section 1 of the Study Guide. See an index of all sections by following the link in this paragraph.
This section of the study guide is intended to provide practice problems and solutions for actuarial students to accompany the pages of Basic Ratemaking cited below. Students are encouraged to read these pages before attempting the problems.
Werner, Geoff and Claudine Modlin. Basic Ratemaking. Casualty Actuarial Society. 2009. Chapter 1, pp. 1-2.
Original Problems and Solutions from The Actuary’s Free Study Guide
Problem S5-1-1. A provider of workers’ compensation insurance insures a company with the following staff:
3 employees earning $80000 per year.
3 employees earning $120000 per year.
6 employees earning $240000 per year.
The insurer uses annual payroll as the measure of exposure and determines that there are 60 exposures. What is the unit of exposure?
Solution S5-1-1. The total insured payroll is 3*80000 + 3*120000 + 6*240000 = 2040000. Since we know that this amount of payroll constitutes 60 exposures, our unit of exposure is 2040000/60 = $34,000 per year.
Problem S5-1-2. Which of these statements is always true?
(a) Written exposures = In-force exposures
(b) Written exposures = Earned exposures
(c) Written exposures = Earned exposures + Unearned exposures
(d) Written exposures = (Earned exposures)*(Unearned exposures)
(e) Written exposures = Earned exposures – Unearned exposures
Solution S5-1-2. The correct answer is (c). Werner and Modlin (1) state the following: “Earned exposures represent the portion of the written exposures for which coverage has already been provided as of a certain point in time.”
“Unearned exposures represent the portion of the written exposures for which coverage has not yet been provided as of that point in time.”
As written exposures can either have coverage provided for them or not have coverage provided for them (the Aristotelian law of the excluded middle), it follows that Written exposures = Earned exposures + Unearned exposures. Clearly, then, answers (b), (d), and (e) cannot be true. Answer (a) is not true because the number of exposures that are actually at risk of loss (in-force exposures) can be less than the number of exposures included in the policies the company wrote (written exposures).
Problem S5-1-3. An insurance company has written premium of $500000 and earned premium of $60000 for a single large insured. What is the unearned premium for this insured?
Solution S5-1-3. We use the following definitions from Werner and Modlin (1):
“Written premium is the total premium associated with policies that were issued during a specified period.”
“Earned premium represents the portion of the written premium for which coverage has already been provided as of a certain point in time.”
“Unearned premium is the portion of the written premium for which coverage has yet to be provided.”
Therefore, it follows that Written premium = Earned premium + Unearned premium, so
Unearned premium = Written premium – Earned premium = 500000 – 60000 = $440,000.
Problem S5-1-4. An insurance company has written premium of $500000 on 300 policies, each of which had the same premium. During the term for which the policies were written, only 250 policies were in effect. What is the in-force premium during this term?
Solution S5-1-4. We use the following definition from Werner and Modlin (1):
“In-force premium is the full-term premium for policies that are in effect at a given point in time.”Since each policy has the same premium and 250 of the 300 written policies are in effect, the in-force premium is (250/300)*500000 = approximately $416,666.67.
Problem S5-1-5. What is the difference between a loss and a claim?
(a) There is no difference.
(b) A loss includes any applicable deductible, and a claim does not.
(c) A claim refers to the demandfor compensation, and a loss refers to the amount of compensation.
(d) Losses require loss reserves, but claims do not.
(e) “Claims” refers to reported losses, and “losses” refers to paid losses.
Solution S5-1-5. The correct answer is (c) A claim refers to the demand for compensation, and a loss refers to the amount of compensation. This follows Werner and Modlin (2), who use “the term claim to refer to the demand for compensation, and loss to refer to the amount of compensation.”
See other sections of The Actuary’s Free Study Guide for Exam 5.