Questions and Answers of Insurance

A large industrial company X wants to insure its properties against the risk of earthquakes, because many of its plants are in earthquake-prone regions.a. Explain why a simple burning cost analysis
Credit risk Modify the algorithm in Section 24.3.2 (b) to take into account changes in the value of the economic factor over the K periods. Assume the values of ψ over the period, ψt, are provided
Personal accident i. Describe the main coverage of personal accident insurance and give an example of a benefit schedule.ii. Mention two composite personal lines product to which personal accident is
Extended warranty (and common shocks)You are a quantitative analyst for Company X, which sells cheap digital cameras at €50 in the European market at a production cost of €20. The cameras are
Answer the following questions about periodic payment orders (PPOs).i Explain what a PPO is.ii Explain why they were introduced, and who is ultimately responsible for deciding whether a PPO rather
Professional indemnity, claims-made policies i. Explain the difference between a claims-made basis policy and an occurrencebasis policy in direct insurance.X is a law firm that buys professional
Your company uses the following table of ILFs.Policy limit (£) ILF 95,238 0.953 100,000 1.000 105,000 1.046 476,190 1.773 500,000 1.785 525,000 1.796 952,381 2.281 1,000,000 2.285 1,050,000 2.289a.
(*) Prove Equation 23.9 directly for the case of the lognormal distribution, starting from Equation 23.2.
(*) Prove that the ILF curves corresponding to the following severity models: (a)lognormal, (b) lognormal/Pareto, (c) lognormal/GPD, (d) empirical/GPD are as in Sections 23.4.1.1–4.
(*) Prove that the CDF of the severity curve above b (conditional on being above b)corresponding to an ILF curve with basis point b is F x b b ( ) = −1 ILF (x b ) ILFb ( ) ’ ’ / .Hint: Start
Assume that the correct severity distribution for a public liability portfolio is a lognormal with μ = 10.5 and σ = 1.2. Derive the analytical form of the corresponding ILF curve above £100,000
Consider the same food manufacturing plant as in Question 12.The underwriting guidelines for food manufacturing plants are also as before, with the following exceptions:• The exposure curves in use
Consider a food manufacturing plant with the following characteristics:• TIV (PD) = £200M, TIV (BI) = £200M, MPL (PD) = £130M, MPL (BI) = £200M• Local deductible (LD) for PD = £1M, LD(BI) =
(*) Calculate the exposure curve corresponding to the cumulative distribution function that incorporates MPL uncertainty (Equation 22.39).
(*) Adapt the algorithm in Section 22.8.2.3 for the simulation of losses for a single location to the case where the exposure curve is defined in excess of the underlying deductible.
(*) Show that it is possible for the KS distance between the CDF of two cumulative distribution functions F x( ) and F x * ( ) with domain [0,1] can be made arbitrarily close to 1 while at the same
(*) Show the connection between the following probability distributions from statistical mechanics: f (ε ε ) = A k / / ( ) exp 1 ( T) − (Bose–Einstein), f (ε ε ) = A k / / ( ) exp 1 ( T)
Given the exposure curve tabulated in Question 6, and knowing that it is a Swiss Re curve with c = 3.0:i. Using Bernegger’s formulae in Section 22.5, verify that the values of the exposure curve
As the actuary for a Lloyd’s syndicate specialising in property reinsurance, you are asked to quote a £3M xs £2M layer for a Risk XL policy, which is covering a portfolio mostly of large
Your house is insured for £300,000 and you pay £500 for your household insurance, which mainly insures your house against fire events. On average, the insurer expects to achieve a loss ratio of 60%
Prove that an exposure curve G(x) is concave in [0,1] in the general case (the one in which F(x) is not necessarily continuous and with defined first derivative over[0,1]).
Consider the curve y xx x = − + 3 2 4 34 32 . Can this be an exposure curve? If so, calculate: (a) the probability of a total loss and (b) the average loss.
According to Equation 22.15, the average loss only depends on the derivative at point 0, regardless of what the curve does afterwards. Therefore, very different exposure curves will give the same
Assume that you have a gunpowder factory which is so badly protected against fire that, once any fire starts, all the gunpowder blows up. (i) Draw the severity curve and the exposure curve. (ii) If
An insurance company X has been writing a mixture of EL and PL business (roughly in the same proportion) over the last 10 years. The summary statistics (for the last 6 years only) are as
You want to adapt the risk-costing process introduced in Section 6.2 so that it works for experience rating of excess-of-loss reinsurance of a liability portfolio, such as employers’ liabilitya.
Company C has purchased risk excess of loss (XL) cover for its property portfolio.A reinsurer R offers a £3M xs £5M layer of reinsurance with these characteristics:a. Losses occurringb. One-year
Modify the algorithm in Section 21.6.2 for the Monte Carlo simulation for a Risk XL contract layer so that it works for a European Indexation Clause.
(*) Prove that the variance of losses to a layer for the case of a GPD severity with a generic claim count distribution is as follows. The formula is quite complex so we’ll need to define a few
(*) Prove Equation 21.13 and generalise it to the case where (a) the severity distribution is Pareto but the claim count distribution is not Poisson; (b) the severity distribution is a GPD and the
(*) Generalise Equation 21.12 to the case where instead of a single parameter Pareto distribution above θ your distribution is made of a spliced Pareto distribution, i.e. a distribution with this
(*) Prove analytically Equations 21.11, and prove that it reduces to Equation 21.12 in the case of a single-parameter Pareto.
Simplify the risk-costing process for Risk XL reinsurance so that it can be used for costing property reinsurance, stripping out all the features that are necessary only for liability reinsurance.
(*) Prove the formulae given in Box 21.1 to extrapolate back the GPD. By remembering that the single-parameter Pareto distribution and the exponential distribution are but special cases of the GPD,
(*) Re-write Equations 3.4 for the case where the policy structure includes an EEL deductible, a limit L, an annual aggregate deductible AAD, and an annual aggregate limit AL.
Three common bases for policies in treaty reinsurance are losses occurring during(LOD), risk attaching during (RAD), and claims-made.i. Explain how these bases work.An annual excess of loss
A medium-sized UK-based insurance company underwrites mainly commercial and industrial property and motor and liability insurance. Outline, with reasons, the types of reinsurance it is likely to buy

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