Pricing In General Insurance 2nd Edition Pietro Parodi - Solutions

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How would you change the Fackler reserve accumulation formula to reflect death benefits payable at the middle of the policy year instead of at the end of the policy year?
A whole life policy uses the simplified net premium method with 1. An annual gross premium per unit of Prem_pu 2. A level death benefit of 1,000 per unit in force 3. A first-year reserve mortality rate of q 4. A first-year reserve interest rate of i 5. Death benefits assumed paid at the end of the
Explain the reserve pattern for a 30-year term policy that would result from benefits that increased faster than premiums increased for the first ten policy years and then increased at the same rate as premiums increased for the next 20 policy years. Construct and graph an example.
Show that adding a 2% of premium expense to all policy years has no effect on reserves at the end of each policy year. Hint: You can calculate the net premium and reserve for this additional expense separately and add it to the net premium and reserve for the benefits and other expenses.
In the discussion of initial expense allowances, it was stated that reserves can be calculated as an accumulation of past net premiums less an accumulation of past benefits and expenses. Using the definitions of net premiums and reserves, develop such a formula. Hint: 0 = PVFB(0)— PVFP(0). Find a
Using the results of all the preceding exercises in this chapter except Exercise 5.2 (Semiannual Premiums) and Exercise 5.9 (Endowment Benefits), summarize cash flows by premiums, expenses, benefits, and total (product) on a per unit issued basis.t Prem(t) Exp(t) Ben(t) ProdCashFlow(t)
Using the results of all the preceding exercises in this chapter except Exercise 5.2 (Semiannual Premiums) and Exercise 5.9 (Endowment Benefits), calculate cash flows at the beginning, middle, and end of the policy year, on a per unit issued basis.| t CashFlowBeg(t) CashFlowMid(t) CashFlowEnd(t)307
Calculate the pure endowment benefit per unit issued, given that a 1,000 endowment benefit per unit is payable to those policies still in force at the end of 20 policy years and given the following survival factors.| t SurvFactor(t) PureEndow(t)18 0.400 19 0.372 20 0.350
Calculate dividends per unit issued, given that dividends are not paid to policies lapsing during the policy year and given the following data.[ t Div_pu(t) SurvFactor(t) Lapses(t) Div(t) |1 0.00 0.9000 0.0990 2 0.50 0.8500 0.0489 3 1.00 0.8250 0.0238
Given the following probabilities of lapse and cash values per unit in force, calculate surrender benefits per unit issued.t Lapses(t) CV_pu(t) SurrBen(t)0.0990 0.00 2 0.0489 2.00 3 0.0238 8.00
Building on Exercise 5.5, calculate claim expenses, given that contestable death claims, which are defined as claims occurring during the first two policy years, cost the company an average of 1,000 per claim, and incontestable death claims (those that occur after the first two policy years) cost
Building on Exercises 5.1 through 5.4, calculate death benefits per unit issued, given a level death benefit per unit in force of 1,000, return of premiums paid beyond the month of death, and the following probabilities of death.t DB_puMid(t) ROPFactor Prem(t) Deaths(t) DeathBen(t)/SurvFactor(t —
Building on Exercises 5.1 through 5.3, calculate maintenance expenses per unit issued, given maintenance expenses of 60 per policy in force at the beginning of the policy year and 2% of premium.t ExpPerPol(t) ExpPrem(t) MaintExp(t)/ AvgSize x Prem(t)
Building on Exercise 5.1, calculate acquisition expense and commissions per unit issued given the following information:* Acquisition expenses of 100 per policy and 50% of first-year premium* Commissions of 80% of first-year premiums and 10% of renewal premiums, and* Sales expenses of 25% of
Suppose that half (call this “AnnualPct”) of the policies will be issued with an annual mode of payment (as in Exercise 5.1) and half (call this“SemiAnnualPct”) of the policies will be issued with a semiannual mode of payment. Next suppose that the semiannual mode of payment has the
Annual Premiums Given a policy fee of 100 per year, an average size policy with 200,000 of death benefit, a unit defined as 1,000 of death benefit, and the following values for premiums per unit in force and survival factors, calculate the premium per unit issued.t Prem_pu(t) SurvFactor(t — 1)1
Using the following single life mortality rates for lives x and y, calculate joint first-to-die and joint last-to-die mortality rates.t qx(t) ay (t) FTDg@xy (t) LTD@xy(t)1 0.0100 0.0050 2 0.0150 0.0070 3 0.0200 0.0090 4 0.0250 0.0110 5 0.0300 0.0130
Building on Exercises 4.1 and 4.7, calculate midyear discount factors and the product of the midyear discount factors times Deaths(t).> DiscFactorMid(t) DiscFactorMid(t) X Deaths(t)BNO- &oHB oe Use the above factors to calculate the present value of a death benefit of 100,000 payable at the middle
Building on Exercise 4.6, calculate the probability of surviving to the beginning of the policy year and then either dying or lapsing during the policy year.t Deaths(t) Lapses(t)FaWFN
Using the discount factors from Exercise 4.1 and the survival factors from the previous exercise, complete the following table.t DiscFactor(t) SurvFactor(t) DiscFactor(t) X SurvFactor(t)0 1.00000 1.00000 1.00000 Using the above results, calculate the present value of annual premiums of 300 per year
Given the following mortality rates and lapse rates, calculate persistency rates and survival factors.t qd(t) qw(t) pb) SurvFactor(t) :0 1.00000 1 0.0020 0.15 2 0.0025 0.10 3 0.0030 0.07 4 0.0035 0.06 5 0.0040 0.05
Adjust the formulas for PVPmt(n) in Formula 4.4.4 to reflect payments that occur at the beginning of the policy year.
Given the following mortality rates, calculate persistency rates and survival factors.t q(t) p(t) SurvFactor(t)0 1.00000 1 0.0020 2 0.0025 3 0.0030 4 0.0035 5 0.0040
Using the factors developed in the previous exercise, calculate the present value of each of the following three sets of cash flows (A, B, and C).t Cash Flows A B G 0 —1,000 100 = 100 1 80 100 40 De 80 100 3h)3 80 100 30 4 80 100 25 5 1,080 0 20
Using the following interest rates, calculate five years of accumulation factors and discount factors.f i(t) AccumFactor(t) : DiscFactor(t)0 1.00000 1.00000 i 0.080 2 0.075 3 0.070 4 0.065 5 0.060
Recalculate the breakeven sales changes in Table 3.5.3 after reducing the premium margins from 70% and 80% to 50% and 60%, respectively.
A company currently sells only UL business. It is considering whether to develop and sell a ten-year term product. The company expects the term product to reduce the sales of its UL products. This will allow one UL underwriter to be transferred to underwriting term products.However, the company
A new blood test has become available that will ‘allow the company to screen out prospective insureds with the newly discovered biathlon deficiency (BAD) condition. The laboratory your company uses for blood testing can now perform a BAD screen. You are given the following information:¢ By
To derive Formula 3.4.1, we assumed that the increase in assets during the year, excluding the portion of the increase due to investment income (equal to B—A —I), earns a half-year’s simple interest (1/2).Show how to develop a more refined version of Formula 3.4.1 using compound interest in
Comparing the segmentation and portfolio methods of crediting interest, which is generally more competitive in a rising interest rate environment? Why? Which is more competitive in a falling interest rate environment?
Suppose you have the following investment choices for constructing a new asset portfolio:AssetClass Gross AnnualDefault Investment Maturity| Yield Cost Expenses (years)Government Bonds 6.00% 0.00% 0.05% 3 Corporate Bonds 7:25 0.02 0.10 10 Junk Bonds 15.00 5.00 0.20 5 To limit its risk in a
If ages 25 to 30 are the peak ages for borrowing money and increasing personal debt and ages 55 to 60 are the peak ages for saving money, explain how demographics might be used to predict the supply and demand for money, decades in advance. What effect would changes in the supply and demand for
Describe five different events that could cause a company’s lapse rates to soar.
Which of each of the following pairs tend to have higher lapse rates?First year/renewal year Issue age 25/issue age 55$10,000 policy/$1,000,000 policy Quarterly premiums/annual premiums Directly billed/ pre-authorized checks Substandard risk/standard risk Smoker /nonsmoker Nonpreferred (residual)
Suppose a block of $1 billion of life insurance issued on December 31, 1999 has the following experience over the next three years:Year Amount Lapsed Death Benefits Paid 2000 $99,000,000 $1,000,000 i 2001 89,000,000 1,000,000 2002 80,000,000 1,000,000 Calculate the lapse rate, mortality rate, and
Refer to Example 3.2.3 at the end of Section 3.2.4.3.a. Recalculate qdActual assuming the expected lapse rate is 25% instead of 15%.b. Recalculate qdActual assuming only 50% of the extra lapses are selective.c. Finally, recalculate qdActual assuming both of the previous changes.
Building on Exercise 3.4, suppose you just discovered that a competitor has a super-preferred category that you think is skimming half of the people with mortality of 85% or less out of your preferred group. What effect has this had on the average mortality of the first preferred group(originally
Suppose everyone in a group of 51 insureds has a different expected mortality percentage. These 51 different percentages are spread evenly from 75% to 125% (that is, one person at every whole percentage).Initially this entire group is placed in the “standard” risk class. You are asked to split
You are given the following information:¢ A group is composed of 75% nonsmokers and 25% smokers¢ The mortality of the overall group is 37.5% of Table XXX, an old, decrepit, but still widely used mortality table¢ Smokers have twice the mortality rate of nonsmokers.Suppose the company offers 50%
Mortality can vary significantly by gender, tobacco usage, and size of policy. Which factor is generally the most and least significant?
Describe the differences between aggregate, select, ultimate, and select and ultimate mortality tables. Which type of mortality table is usually the most appropriate for use in developing life insurance products?
Assume that you are the product manager for your company’s universal life line of business. One of your junior actuaries has recommended that the cost of insurance charges for a block of UL policies that have been in force for five years be increased 10%. You ask for reasons why they should be
~ You have worked with the marketing and sales staff to develop the following grid of premium levels and profit margins. The company has been growing premiums at 15% per year and would like to continue to do so. The company will collect 350 million of total premiums this year. Examine the effect of
You are the actuary for a medium-sized company, with sales distribution concentrated in the Northwest. Your company primarily sells term insurance, concentrating on middle-income workers. Your underwriting process is very efficient, and mortality results and profits have been excellent for several
What types of market research do you think are the most essential?Why?
Name the competitor-oriented pricing strategy employed in the following situations:l. Company A is absolutely committed to having the lowest-cost term product on the market. Monitoring of the competition is constant.Changes in price can be made within a matter of weeks. Fifty percent market share
Explain the buyer-oriented pricing strategy employed by each of the following companies:1. Company A carefully sells products under a well-recognized name to people with incomes in the top 10%. Similar products, with prices roughly 20% to 25% higher, are sold to a lower-income market by a different
How would you organize the product development function? Why would you organize that way?
What core competencies would be most important for the following products or markets?1. Level term insurance 2. Debit or home insurance sales 3. High-income market 4. Universal life insurance.
Using the target market attributes discussed in Section 2.2.1, explain why each of the following would not be considered good target markets:1. Sales to be made through a variety of distribution channels, including telemarketing, the Internet, and agent solicitation 2. Persons belonging to and
Which distribution channels are best suited to the following types of sales?a. A sophisticated use of life insurance to solve estate-planning needs.b. Burial insurance for someone without a checking account but with an employer willing to withhold funds from paychecks to pay life insurance
Describe the ideal tax treatment of life insurance if the goal is to encourage the public to use life insurance as a savings and protection vehicle.
Calculate the following VUL policy’s account value on May 31, given the following information:Life Insurance Products and Finance On April 30: Account value = 5,500 and unit value = 55.0000 On May 10: Cost of insurance charge = 25.00 and unit value =50.0000 On May 31: Unit value = 55.2729 Repeat
Calculate the following UL policy’s account value on May 31, given the following information:Annual interest crediting rate = 6.00%On April 30: Account value = 5,500 On May 10: Cost of insurance charge = 25.00.
A company designs a life insurance policy with the following prescheduled premium pattern: annually increasing premiums designed to cover only mortality, expenses, and profit for the first 20 years, followed by level premiums for the remainder of the insured’s life. The death benefit remains
Describe at least three ways to receive cash from a life insurance policy while keeping the policy in force. Consider all the different types of products and product features.
For dynamic products, if the cash value accumulates to exceed the original death benefit, what amount is paid upon death?
Explain how cash values develop on dynamic products. Why would two dynamic policies with the same death benefit, risk class, gender, and issue age develop different values?
For a participating whole life product, how can two policies with the same initial death benefit, risk class, gender, and issue age develop different values over the life of each policy?
Explain why cash values develop on permanent, whole life products, and why they are the same rate per thousand of insurance for each buyer of the product with a given risk class, gender, issue age, and policy year.
Give an example of a personal lines insurance liability product, and explain what it covers.
Explain briefly what these liability insurance products cover: employers’ liability, public liability, aviation liability and professional indemnity, and give two examples of claims for each of these products.
Describe what the legal framework of liability insurance is and how the principle of indemnity applies to liability insurance.
It is stated in the text that the principle of indemnity cannot be applied to the case of personal accident because loss of life, health or limb cannot be quantified. How is it that it can be applied to the case where these same losses are caused by a third party, in liability insurance?
Doing some personal research, explain what air traffic control liability is.
What do these two aviation insurance policies cover?a. Loss of licenceb. Loss of use
What is jewellers’ block insurance?a. What does it cover exactly? (Find out specific policy summaries or articulate descriptions from actual insurers.)b. Why do you think there is a need for it?c. How would you classify it in terms of cover?d. What do you think are the main risks involved?
What is a bankers’ blanket bond policy?a. Why is it called a ‘bond’?b. Why is it called ‘blanket’?c. What does it cover exactly? (Find out specific policy summaries or articulate descriptions from actual insurers.) Try and capture the overall coverage in a matrix like those in Section
What is specie insurance?
Find out what the policy ‘IT All Risks’ is and what it covers. How would you classify it according to the PRA scheme?
Find out who the main specialist suppliers of credit insurance are, then pick one of them and make a list of the products they offer.
Can you explain the difference between employers’ liability insurance and workers’compensation insurance? Name three countries where employers’ liability is sold and three countries where workers’ compensation is sold.
Find out how non-life insurance obligations are classified according toa. Lloyd’s of Londonb. The Solvency II regulatory regime being proposed by the European Union by doing personal research. (Hint: for Solvency II, you can refer to the Quantitative Impact Study 5 ‘QIS5’ or any updates that
A UK company writes a commercial motor fleet policy for a company Y in Freedonia, which has suffered from high inflation in the last few years. You have been given the list of the five losses notified to Y in the last few years.As part of your pricing exercise, you have to prepare appropriate input
How would your answer to Question 1 have changed if you also had available statistics on the distribution of contents insurance losses over the year, and you knew that• 22% of the losses occur between January and March.• 25% between April and June.• 30% between July and September.• 23%
Calculate the revalued amount of the three losses, stating all additional assumptions you have made.Year Month Index value Year Month Index value 2010 Sep 114.9 2012 Jan 121.1 Oct 115.2 Feb 121.8 Nov 115.6 Mar 122.2 Dec 116.8 Apr 122.9 2011 Jan 116.9 May 122.8 Feb 117.8 Jun 122.3 Mar 118.1 Jul
You decide to revalue three contents insurance losses to the midpoint of an annual policy that will incept on 1 June 2013 by using the consumer price index (CPI).The losses occurred in the United Kingdom on September 2010, March 2011 and February 2012 and the amounts are £1500, £3400, and £2200,
The following table shows a few statistics related to the loss amount distribution for a risk over the period 2014 to 2023. The loss amounts from which these statistics are derived were generated from a lognormal distribution with parameters 10.3 and 1.5. For each year, a fixed number of 500 losses
Explain what index (or what flat rate) you would use to revalue the following types of cover, doing personal research where necessary.i. Marine Cargo cover for ships transporting (i) oil or (ii) cigarettes ii. Contents insurance (UK)iii. Personal accident insurance with fixed benefits iv.
What information would you request to price (a) commercial motor risk and(b) professional indemnity risk?
To enable yourself to price aviation risk, you decide to build a database of large aviation losses. (a) What information would you seek to include in the database?(b) Where would you look for that information?
With a foray in the necessary chapters on reinsurance and rating factor selection, describe in what ways the claims data used for pricing personal lines insurance, commercial lines insurance, and excess-of-loss reinsurance are likely to differ.
Find out the payouts and circumstances of the five most expensive car insurance claims in the United Kingdom’s history.
Choose a medium-sized UK insurer and try to reply to the following questions: What lines of business are they writing? What are their total revenues? How many employees do they have? What was their gross written premium in 2012? What was their operating ratio? What was their expense ratio?
Choose a large high-street retailer Y and find as much as you can about it by looking at public information on the Web, including their financial statements. What is their territorial distribution? Are they present abroad? What have their revenues been in the last 4 to 5 years? How many employees
On the Internet, look up the list of the top 5 pharmaceutical companies and pick one of them. Let us call that company X. Now imagine that X has come to your underwriter for a quote for product liability. Find out as much as you can about the exposure of X to this risk and answer as many of the
Describe briefly all the steps of the standard risk costing process based on the collective risk model for the experience rating of a portfolio of risks (e.g. a company which takes a motor insurance policy), including inputs (types of data) and outputs.Feel free to use a flowchart or a list as you
One of the most popular risk models for pricing is the collective risk model for total losses, S.a. Explain what the collective risk model is and what its underlying assumptions are.b. Discuss the validity of the collective risk model’s assumptions when used to model employers’ liability
(*) Prove that for the collective risk model (S) = (X) (N) and that ????(S) = (N)????(X) + ????(N) (X)2 using the moment generating function MS(t) of S. In the formulae above, N, X and S are the random variables for the number of claims, the severity, and the aggregate losses,
Doing personal research, find the list of the top 10 natural catastrophes by death toll and by insured losses in the last 30 years. Comment on how similar these two lists are.
Is space weather more or less predictable than terrestrial weather? Why?
Identify, for each of these territories, the two or three most likely natural catastrophe events and discuss if the risk is homogeneously spread over the territory or localised in a specific area:a. United Kingdomb. United Statesc. Japand. Italye. Germanyf. A territory of your choice
It is now illegal in the United Kingdom (and the rest of Europe) to use sex as a rating factor, for example, in motor insurance. Still, there are some insurance providers, which were traditionally aimed at the women’s markets, that are still around.Do some personal research to check what happened
A large UK-based pharmaceutical company is reviewing its risk management strategy.a. Write down the insurance products that it is likely to consider purchasing to limit the volatility of its results, briefly stating why they are relevant to the company’s risk management structure.b. Explain why
Find out the name of the so-called ‘big four’ consultancy firms and find out the scope of their advisory activity: is insurance advice the main source of their business?What else are they advising on? Pick one of these large consultancy firms and try and find out how many actuaries work for it.
Go on one of the major aggregators’ websites and get a quote for a pet insurance or a travel insurance policy. What questions are you asked? How are the policies different apart from their prices?
Find out who the top 4 insurance aggregators in the UK are, and for each of them, find out (i) their total revenue; (ii) what types of coverage they offer and (iii) what their relative position is as sellers of motor insurance, home insurance, and travel insurance.
Find out who the 10 top reinsurance brokers in the world are by total revenues.How does that tie up with the list of the 10 top insurance brokers? What are the main differences?
Find out who the 10 top insurance companies in the world are by net premium written (or other relevant measures) and the top 10 reinsurance companies (by the same measure).
The same company X described in Question 1 buys employers’ liability insurance from the ground up. Through a fronting arrangement, the captive reinsures all losses of less than £100,000. All the rest is ceded to the insurance market.Describe who pays how much in the case of these (accepted)

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Pricing In General Insurance 2nd Edition Pietro Parodi - Solutions

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