ERRATA CORRIGE

Acknowledgements

Many thanks to the following people for spotting a good number of the errors listed here: Michael Fackler, Raymond Poole, Arun Srikrishna Vihar, Andrei Kobelev, Otto Beyer.

Preface

• • Page xxii – At the end of page, the sentence should end thus: "the correlation between these risks is important"

  • Page xxiii  – "retir'd from any mortal sight" should actually be "retir'd from any mortal's sight"

Chapter 2

• • Page 26 - fourth-last row: "Excess of loss (XL)" should read "Risk excess of loss (Risk XL)"

Chapter 3

• • Page 47, Figure 3.1: the Retained before AAD for Loss 4 should £73,000

  • Page 47, Figure 3.2: the Retained above limit amount for Loss 1 should be £550,000

  • Page 53 -Section 3.3.2.1.4, row 5: replace "Reinsurers, therefore" with "Reinsurers writing excess-of-loss liability products, therefore"

  • Pages 55, Section 3.3.2.2.

  • The current wording:

  • This is a type of XL reinsurance which is similar to the Risk XL, except that it is triggered when the aggregate (rather than individual) losses consequential to a given event exceed a certain amount.

  •  

  • The purpose of Aggregate XL is to protect the insurer from the accumulation of a number of risks which individually may not be relatively small (for example a number of cars being destroyed by a flood, each of which costing between £3,000 and £60,000) but whose total payout may be very large.

  •  

  • should be slightly expanded (for correctness) to this:

  •  

  • The term "Aggregate excess of loss (Agg XL)" means different things to different practitioners and organisations. For some, Agg XL is simply a Risk XL cover where an annual aggregate deductible is retained by the reinsured (see Section 3.3.2.1.2).

  •  

  • For others, it is a type of XL reinsurance similar to Risk XL, except that it is triggered when the aggregate (rather than individual) losses consequential to a given event exceed a certain amount. In this section we will focus on this latter meaning of Agg XL, which also blurs into stop loss cover (Section 3.3.2.4).

  •  

  • The purpose of Agg XL is to protect the insurer from the accumulation of a number of risks which individually may not be relatively small (for example a number of cars being destroyed by a flood, each of which costing between £3,000 and £60,000) but whose total payout may be very large.

  • The standard structure looks like Risk XL: for example, £1m (aggregate) xs £1m (aggregate).  However, the structure may include an interior excess as well, in the sense that the aggregates may apply only to losses exceeding a certain amount. This of course simplifies the management of this cover as small losses do not need to be recorded.

  • Pages 57, Section 3.3.2.4. At the end of the first paragraph, replace "Alternatively, the cover might be based on a monetary amount" with " Alternatively, the cover might be based on a monetary amount, in which case it is sometimes referred to as Agg XL (see Section 3.3.2.2)"

Chapter 10

• • Page 126, just before Section 10.2.1.1: 1.05^(2015-2029)=1.34 should read 1.05^(2015-2009)=1.34 (2009 is the policy year for the claim occurring on 21 March 2010, since the policy incepts on 1 Apr)

  • Page 128, Fig. 10.3, fourth claim: the loss date should 11/1/2010 (US format) and not 11/1/2007

  • Page 130, first bullet point: "2002" should read "2005"

Chapter 11

• • Page 134, third bullet point. "As at date" should read "30 November 2014"

  • Page 136, Fig. 11.3. There is a number of problems with this figure: (a) the Policy year column in the second of the two tables should read 2005–2015 (consistently with the Fiscal year column) instead of 2002-2012; (b) the Turnover columns in the second of the two tables should show £ as the currency; (c) the Turnover revalued at 4% p.a. shows the unrevalued values.  Note that the correct values for this table are shown in the spreadsheet version of the table in the Downloads section of this website (Chapter 11 - Burning cost calculations).

  • Page 137, Section 11.1.6. The title should read "Make adjustments for IBNR and IBNER"

  • Page 141, Fig. 11.6. The phrase "£5m, equal to the individual policy limit" should more accurately read "£5m, equal  to the each-and-every-loss limit for the policy"

  • Page 141, Fig. 11.6. "The only years for which the aggregate deductible has an effect are 2007 and 2008" should read "The only years for which the aggregate deductible has an effect are 2010 and 2011".

Chapter 13

• • Page 172, Figure 13.6, the last sentence in the legend should read: "For example, Ultimate (2012) = 177 x 1.152 = 203.90."

  • Page 175, in the equation for n(2012), 4/12 and 8/12 should be swapped

Chapter 15

• Page 218, Section 15.4, Question 1: Replace the text

Describe three methods for dealing with IBNER when producing the input losses for a severity model, and explain advantages and disadvantages of each method.

• • 1. Describe in one sentence for each, three methods for dealing with IBNER when producing the input losses for a severity model.       

With this text:

You need to produce the input losses for a severity model.

• • 1. Describe three methods for dealing with IBNER when producing such input.  

Chapter 16

• • Page 235, Section 16.5, 1st bullet point: "logn" should read "lognormal"

Chapter 19

• Page 282, Figure 19.3, third row. Replace the following list:

• • • Claim expenses (both LAE and ULAE)

    • Commissions

    • Reinsurance premium

With this new list:

• • • Claim expenses

    • Underwriting and general expenses

    • Reinsurance premium

• Page 283, Section 19.1.3. Replace this text:

Claim expenses

This refers both to expenses allocated to specific losses such as lawyers’ fees, claims management costs (allocated loss adjustment expenses, or ALAE), and unallocated costs such as policy administration, IT, accounting, cleaning, electricity (unallocated loss adjustment expenses, or ULAE).

If ALAEs are already included in the claim amount (as is often the case) we only need to add an allowance for ULAE.

Commissions

This is the amount paid to a broker or to an external agent for procuring the business.

With this text:

Claim expenses

This refers both to expenses allocated to specific losses such as lawyers’ fees, claims management costs, and unallocated costs such as claims department overhead.

Underwriting and general expenses

            These include such items as commissions and brokerage (i.e. the amount paid to an agent or a broker for procuring the business), other acquisition costs (e.g. marketing), taxes, and general expenses (e.g. policy administration, accounting, IT, cleaning, electricity).

Chapter 20

• • Page 311, Point ii: the phrase "for the reinsurer" can be omitted

  • Page 313, just before Section 20.2: "incept over" should read "incept uniformly over"

    • Page 318, just before Equation 20.3: "– that is, claims occur uniformly over the period of the policy," should read "– that is, claims occur uniformly over the period of the policy –"

• Page 320, Section 20.4.1, end of first paragraph:  "development triangle or similar structures"  should read "development triangles or similar structures "

• Page 326, second paragraph: the sentence "Because this is not common in liability reinsurance, there is no need to consider layer indexation" should be removed as it is repeated almost verbatim a few sentences later.

Chapter 21

• • Page 331, first sentence: "Exposure is a method" should read "Exposure rating is a method"

  • Page 331, Section 21.1, at the beginning: the sentence "One way to price property risk for a portfolio of property is" should read "One way to price a Risk XL for a portfolio of property risks is"

  • Page 332, Section 21.1, Point 3 in the list, at the end: "made by a single large industrial plant or 100 small offices" should read "made by a single large industrial plant, or 100 small offices instead

  • Page 332, near the end: "(let us say its MPL)" should be deleted

  • Page 332, footnote, end: "(the list of properties along with their properties)." should read "(the list of properties along with their MPLs)."

  • Page 336, Figure 21.3 (legend): "jumps from approximately 75% to 100%" should read "jumps from approximately 85% to 100%"

  • Page 338, right after the legend of Figure 21.4:  "for which the probability of a total loss is not finite" would read better: "for which the probability of a total loss equals zero"

  • Page 346, Figure 21.7, the numbers displayed as "99.9%" in Columns G and H in the table should be replaced with "100%"

  • Page 354, Section 21.9, last point: "because the curves" should read "because such curves"

  • Page 355, Question 7, Table, Column 4: "Total sum insured" should read "Total premium"

Chapter 22

• • Page 357, first paragraph: "Miccoli" should read "Miccolis"

  • Page 365, first paragraph: "assume a given wage inflation" should read "assuming a given wage inflation"

  • Page 365, Section 22.5.4, replace "for all claims from different claims from the same event" with "for all claims arising from the same event"

  • Page 366, second row after Equation 22.16: "where E(N)" should be deleted

Chapter 23

• Page 410, Question #2: Delete the words "Exam-style question: "

Chapter 26

• • Page 461. Before and after Equation (26.8), replace: "The observed values of Y will then be of the form [...] where epsilon (the noise) has a probability density distribution of the form:" with "The observed values of Y can then be written informally as [...] where epsilon indicates noise, i.e. departure from the expected value E(Y). Equation (26.8) should be read as follows: the observed values of Y are distributed according to the following probability density distribution:" (Comment: Although this way of writing Eq. (26.8) was simply meant as an intuitive way of illustrating the noise term, I found it gave the wrong idea that the noise was additive and that, e.g., a Poisson noise should have zero mean. This should clarify.)

  • Page 464, last two rows: "Assume that the claim frequency is proportional to the annual mileage" should read "Assume that the claim frequency is proportional to a power of the annual mileage" (Comment: otherwise, this constrains beta_3^(3) to be equal to 1!).

  • Page 465. At the end of Section 26.3.4 this sentence should be added.  "Note that if in the two examples above the noise model had been a two-parameter model such as Normal or Gamma (see, e.g., Section 26.3.6), then the dispersion of the model should also be calculated from the data, and the number of parameters would be 8 in the non-interacting and 12 in the interacting case. "

  • Page 465, Section 26.3.5, second paragraph: replace "whose objective is to build exact models" with "whose objective is to build models

  • Page 467, Section 26.3.5.4, first paragraph:  "the variable that increases the variance" should be replaced with "the variable that reduces the variance"

  • Page 470. Equation (26.15): ν = exp(−3−0.3 ×Age+0.2 ×Age+0.15 ×Region−0.4 ×NCB+0.1 × Profession should be replaced with: ν = exp(−3−0.3 ×Age+0.2 ×Sex+0.15 ×Region−0.4 ×NCB+0.1 × Profession)

  • Page 470: the sentence ending "… Dumb3 and all binary. ", should be replaced with "… Dumb3 and all binary. Note that we are making here the simplifying assumption that the dependency of

• •  on these variables can be approximated through a simple monotonic (linear) relationship, so that each factor contributes one parameter only to the overall model and that explains Figure 26.18 and the machinery for categorical variables developed in Section 26.3.4 is not necessary."