Corrections to Modern Actuarial Risk Theory

Corrections to

Modern Actuarial
Risk Theory
-- Using R

by Rob Kaas, Marc Goovaerts, Jan Dhaene and Michel Denuit

Latest update: February 19, 2012

We try to keep this list of typos and minor improvements up-to-date and as complete as possible.
If you find more, please notify us.
For more information, see the book's homepage

Denuit, Goovaerts, Dhaene, Kaas [Lisbon, 2002]
 
We thank the following users for their contributions:

Corrections to be made to the edition with preface dated March 22, 2009 (softcover ed.)

p. 16, l. 1: change φ(x) into φ(d).

p. 51, l. 13: change a(n+1) into −a(n+1)

p. 80, l. 9: change f(s) in the numerator into p(s);
also, change s=1,2,... into s=2,3,...

p. 124, l. 4-5: Delete "Let ... and"

p. 170, l. 9: change "iid" into "identically distributed"

p. 217, l. 11: replace this line by: "wjΣ/wΣΣ for Xjw is equal to the credibility weight zj/zΣ."

p. 277, l. −4: scratch βj

p. 278, l. −5: replace 3.20 by 3.23

p. 280, formula (10.17): replace 0.46 by 0.49 (= 0.42 × 1.17)

p. 293, ex. 10.4.7, l. 4: Table 10.7 should be Table 10.6.

p. 305, l. 13: replace "σ2 = φV(μ)" by "σ2 = φV(μ)/w, with w the weight and"
ibid., formula (11.17): after the first two summation signs, add "wi"

p. 309, l. 6: scratch "ratio"
ibid., l. 8: scratch "ratio" as well as "and saturated model"
ibid., l. 15: delete "other values of p, the proof is omitted, but for"

p. 350, l.-3: replace "1+p/2" by "(1+p)/2"

Corrections to be made to the edition with preface dated May 18, 2008

(see also the corrections for the newer version)

p. 9, l. -1: change "∫ gF" into "∫ fG"

p. 13, Fig. 1.3: The boundary (μ(d),σ2(d)), d>0 of the gray area of possible I(.) should be a graph below the diagonal, not above it. This can be inferred from the fact that the retained claims for proportional reinsurances have a variance proportional to their squared mean.

p. 14, exercise 1.2.9: replace "P−" by "P+" (2x)

p. 63, (3.72) and (3.73): change "ni!" into "yi!"

p. 66, 2nd script: change "max=T" into "maximum=T"
p. 99 and 111, in the script: in the call of uniroot, change "low=" into "lower=", "up=" into "upper=".
R 2.6.0 and higher insist on the full versions of these arguments.

p. 63, l.1: replace "3.9.17" by "3.9.16"

p. 69, p. 380: "SuppDist" should be "SuppDists"

p. 71, below (3.97): replace "Z is mixture" by "Z is a mixture"

p. 95, l.7: replace "Corollary 4.3.5" by "Theorem 4.3.6"

p. 197, exercise 7.3.19: "(0,½)" should be "[0,½]"

p. 198, exercise 7.4.7: "3.7.6" should be "3.8.6"

p. 201, script of exercise 7.7.7: replace "mu.V" by "mu.Z" (3x), "Sigma.V" by "Sigma.Z" (4x)

p. 222, below script: replace "a.." by "a.hat.old" and "a." by "a.hat"

p. 244, 2nd table, bottom line: replace "29.??" by "28.??" (twice)

p. 251, next-to-last line of paragraph starting with "From the output...": replace "0.464+0.58443" by "0.4643+0.5844".

p. 260, Table 9.9: The loss percentages should actually be:
53 58 58 59 62 64 63 57 59 62 53 52 50 53
58 60 58 58 58 57 57 55 56 54 53
56 57 56
58 57 55
119 49 73
52 67

p. 263, exercise 9.5.2 is correct as it is! No correction needed.

p. 264, exercise 9.6.6: in the second-to-last line, replace "nCl" by "TotCl" (3 times).
Also, replace "nCl=0" by "TotCl==0" (with a double equals sign).
In fact, the whole sentence starting with "In a Gamma family" can be scratched; there are no problems in this situation with current versions of R.

p. 264, exercise 9.6.7: replace "under 56%" by "up to 56%"

p. 271, l.-8: "1+j−1" should be "i+j−1"

p. 278, l.-7: Add the following paragraph:
"Note that it cannot be ruled out that there actually is a calendar year effect, if only because model I is already significantly better than II if a significance level 6% is chosen instead of 5%. Doing "plot(k,residuals(glm(Nij~i+j, poisson)))" reveals that the residuals for k=3 are all well below zero. Indeed adding one extra parameter γ3 decreases the deviance substantially. Whether this improvement may be called statistically significant on 5% level is another matter, because specifically choosing this calendar year k=3 was inspired by looking at the data. So, actually, the deviance difference is the maximum of many (one for all models implicitly considered) marginally χ2 distributed random variables that, though probably related, are not comonotonic. Therefore the probability of a Type I error is no longer 5%."

p. 278, Table 10.7: In every number that has more digits than appropriate, change `10.' back into `9.'. In fact the fitted values in the table should read:
2010 102.3 140.1 59.4 25.2 10.7 4.5 1.9 0.8
2011 101.6 139.2 59.1 25.0 10.6 4.5 1.9 0.8
2012 124.0 169.9 72.1 30.6 13.0 5.5 2.3 1.0
2013 150.2 205.8 87.3 37.0 15.7 6.7 2.8 1.2
2014 170.7 233.9 99.2 42.1 17.8 7.6 3.2 1.4
2015 159.9 219.1 92.9 39.4 16.7 7.1 3.0 1.3
2016 185.2 253.8 107.6 45.7 19.4 8.2 3.5 1.5
2017 168.0 230.2 97.6 41.4 17.6 7.4 3.2 1.3

p. 278, p. 279, p. 281: To the `Year of origin' column in Tables 10.7, 10.8 and 10.10, add 10 years to conform with Table 10.1. So change `2000' into `2010', and so on.

p. 293, exercise 10.5.2, l. 3: "Exercise 10.2.4" should be "Section 10.7"

p. 308, l.10: replace "maximizing the expressions" by "minimizing the expressions"

p. 320, 1st line of script: replace "require(statmod)" by "require(tweedie)"

p. 361, l.4: "1982" should be "1972"

p. 361, l.14: replace "in described" by "is described"