Questions and Answers of Insurance

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
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
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.
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
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
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.
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
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
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
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
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
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)
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
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
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
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?
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
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
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
(*) 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
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.
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
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,
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
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
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
A company X (whose main offices are in London) has three business units: one in Gloucestershire, one in Essex, and one in Yorkshire. The company buys property insurance through a captive. Each
(For some readers, this problem might be better tackled after reading Chapter 22.)Petrochemical company X insures its single oil refinery with insurer Y and its property damage insurance has just
(*) The Venn diagram below shows symbolically a portfolio at two successive underwriting years. The shaded area (intersection) ℘′ ∩℘ is made of the contracts that have been renewed; the area
You are monitoring a small portfolio of marine hull policies. The following table gives a snapshot of the portfolio for contracts written during 2019 (left) and 2020(right).Year 2019 Year 2020
Suppose that your gross aggregate loss distribution for a contract can be well approximated by a lognormal distribution with µ = 13, σ = 2 (outputs in USD). The contract covers losses to the layer
Prove that TVaR is a coherent risk measure if the underlying probability density function of the loss distribution is continuous.
You are asked to help your underwriter with an actuarial quote for an aviation liability policy. Your actuarial model produces yearly expected losses of £1.2M.To produce an estimate of the technical
As a result of a pricing exercise, you produce the following estimates for a public liability risk:a. Expected losses = £850kb. Allowance for uncertainty = Nonec. Other costs = £150kd. Commissions
As the consulting actuary for WWW, you have produced the following gross loss model for their public liability (PL) risks. The model is based on 1000 groundup losses (min = £150, max = £1,280,000)
(*) Write down Equations 17.22–17.25 for the case where the frequency model is Poisson and the severity is a spliced Lognormal/Pareto or a spliced Lognormal/GPD.
(*) Write down Equations 17.24 and 17.25 for the Poisson/Lognormal case.
(*) Prove Equation 17.21. Hint: write g0 = Pr(S = 0) as an infinite sum Pr P S Nr P n X r X X N n n( = ) = = ( ) ( + + + = N = ) =∞0 0 ∑0 1 2  | and note that for a sum of positive-definite
R-based question. Your aggregate loss model is a compound Poisson/lognormal model with parameters λ = 5 (Poisson rate) and μ = 10.2, σ = 1.2. Using R and the FFT algorithm given in Appendix B, you
R-based question. Modify the R code in Appendix A so that it is able to deal with(a) a negative binomial distribution for the frequency; (b) a spliced lognormal/GPD severity distribution; (c) a
You are a quantitative analyst for Company X. Company X sells cheap digital cameras, which are sold at €50 in the European market and have a production cost of €20. The cameras are offered with a
You are an actuary for a commercial lines insurance company. One of your jobs is to set the annual aggregate deductible (hence ‘the aggregate’) for commercial policies at a level that is
Gaussian approximation (either computer-based or using numerical tables). Suppose that losses can be modelled according to the frequency/severity model described in Question 2 (frequency: Poi(4.4),
Monte Carlo simulation (computer-based exercise). Assume that losses related to public liability are generated according to this process: next year, the number of losses will come from a Poisson
Basic statistics for the collective risk model. An actuary has analysed company X’s motor third-party liability losses for next year by modelling the number of losses as a negative binomial
(*) Effect of claims inflation on various distributions. Show that applying an inflation of r% to all the losses (i.e. X X ’ = + (1 r)) modelled by:• a Lognormal distribution with parameters µ
(*) Show that the single-parameter Pareto, F x x ( ) = − θ α, and the Type-II Pareto,, are both special cases of the GPD, F x x ( ) = − +  −.
In Section 16.4, we have justified the use of the empirical distribution to represent attritional losses on the basis of the Glivenko–Cantelli theorem and the Dvoretzky–Kiefer–Wolfowitz
Do the following:• Calibrate (i.e. find the parameters of) the Lognormal distribution based on these losses, pretending you do not know what the original parameters were.• Calculate the mean, the
The following losses have been generated from a Lognormal distribution with parameters μ = 10 and σ =
Discuss the advantages and disadvantages of a frequency/severity model in comparison to a burning cost approach that includes adjustments for inflation, exposure, etc.
As a result of the overall IBNER analysis, you produce the following cumulative IBNER factors.Development years IBNER (cumulative)1->onwards 2.44 2->onwards 1.32 3->onwards 1.20 4->onwards 0.95
You need to produce the input losses for a severity model.i. Describe three methods for dealing with IBNER when producing such input.ii. Explain the advantages and disadvantages of each method listed
(*) Discuss (a) how the relationship p pa bk kk−= +1, which holds for the Panjer class variates, can theoretically be used to determine whether realisations from a count process should be
The table below (Case 1) shows the number of employers’ liability losses reported to an organisation over the period 2017 to 2024, and the relevant exposure over the same period. Some IBNR factors,
(*) Prove that the Poisson distribution, the binomial distribution, and the negative binomial distribution all satisfy Equation 14.1 and find the values of a and b in terms of the parameters of these
(*) Prove that Equation 14.5 holds true if Conditions 1 through 4 in Section 14.2 are satisfied. Also prove that if Conditions 1 and 3 are satisfied and Equation 14.5 is satisfied, then Conditions 2
Using a spreadsheet, simulate a random number of claims from a Poisson process using the property that the interarrival time of claims from a Poisson process is an exponential distribution. Hint: Use
(*) Show that when the tail distribution is a Generalised Pareto distribution (see Chapter 16) with null threshold: F x x ( ) = − + a. the tail factor and the projected/ultimate ratio are as
The following table records all claims that occurred from 1 April 2010 and were reported by 31 October 2013.Loss ID Occurred Reported Delay (days) Delay (years)R01 29/7/2011 21/12/2012 511 1.399 R02
You are given the following claim count triangulation, providing the number of claims occurred in each policy year and are reported within a certain number of development years.Development Year 0 1 2
(*) Show how Equation 11.7 can be justified as an approximation of the formula for the total expected losses (S x ) = × f x( )dx∞∫ λ0 where λ is the expected number of claims from the
Show how the burning cost formulae shown in Section 11.1.12:a. simplify in the case where there is no annual aggregate deductible (AAD = ∞);b. should be amended if an annual aggregate limit AAL is
Consider a simple loss process where the number of claims follows a Poisson distribution with rate λ = 5 and the individual claim amount follows a lognormal distribution with µ = 11 and σ =
As part of a pricing exercise for a Commercial Property Risk XL programme incepting on 1 January 2016 and written on a losses occurring basis, you have to calculate the earned premium for a number of
A medium-sized UK-based company (A) is currently insuring its public liability risks with an insurance company (B). You have been asked (as a consulting actuary) to advise company A on whether or not
In Box 11.2, we say that the standard way of calculating the average development ratios in the chain ladder is a weighted average. What weights are used in the definition of D(0→1) (and, for that
In Box 11.2, we have seen that in the standard chain ladder method, the weighted average is normally used to calculate the average development ratios between two successive development years.a.
In Box 11.1, we have introduced weighted statistics for the empirical mean, standard deviations, and the percentiles of a data set. Show that by setting all weights to 1, the formulae for the mean,
The underwriting manager in charge of Energy has asked you to build a model to cover operations all risks (OAR) for Offshore Windfarm. This model will cover property damage (PD) only.As a starting
Explain the rationale behind the four different possible formulations of the total cost of risk given in Equations 30.3 and 30.4, and their relative advantages and disadvantages.
Company X has traditionally purchased public liability insurance from the ground up, but to decrease the insurance premium (currently at £2,500,000) spend and in view of its financial robustness, it
Consider the following list of insurance structures and highlight those that are surely inefficient using VaR@99% as a measure of volatility:a. Structure 1: premium = £1.2M, VaR@99% = £99Mb.
Monkey business. Assume that you own an establishment with a troop of 120 macaques (on average) that you sell as domestic pets and that the probability of one of your monkeys dying in a normal year
Calculate the theoretical tail correlation for the copula of Question 4.
Do the same as in Question 3 but combining the two vectors with a t copula with a desired correlation of 0.6 and ν = 1.3.
Using a spreadsheet, generate two random vectors of 1000 elements each, with each element coming from a lognormal distribution. Then combine them with a Gaussian copula, producing a rank correlation
Create two vectors X, Y such that Y = f(X) (and are therefore fully dependent) but have zero linear correlation.a. Can you produce an example for which the linear correlation is equal to 0?b. Can you
In the table below, X and Y represent the property damage and bodily injury components of 19 motor third-party liability losses.a. Calculate the linear correlation and the rank correlation
Compare advantages and disadvantages of analysing a risk (such as motor) by splitting it into its main components (such as own damage, third-party liability for motor).
Explain (a) the difference between categorical and non-categorical factors; (b) the reason why, when the number of levels of a categorical factor becomes large, using GLM may become difficult; and
A general insurance company that writes Fine Art insurance has decided to use its historical loss data to replace the current model (mostly based on underwriters’experience and judgment) with a
Your company decided a few years ago to enter the lucrative business of selling alien abduction policies. This business has performed extremely well in the past, with an observed loss ratio
You are the actuary for a reinsurance company. An insurance company, A, wants to buy a layer of excess-of-loss reinsurance (£10M × £5M) for its property portfolio from your company. The
(*) Prove that Bayesian credibility estimate – when the number of claims of a client follows a Poisson distribution and the prior distribution for the Poisson rate follows a gamma distribution –
(*) Using the Bayesian approach to credibility, prove that the posterior distribution of Θ given s (see Section 26.3.2 for the meaning of these parameters) is itself a normal distribution with these

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