CDR: One year claims development result

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/CDRMethods.R

Description

Standard deviation of the claims development result after one year for the distribution-free chain-ladder model (Mack) and Bootstrap model.

Usage

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CDR(x, ...)
## S3 method for class 'MackChainLadder'
CDR(x, dev=1, ...)
## S3 method for class 'BootChainLadder'
CDR(x, probs=c(0.75, 0.95), ...)
## Default S3 method:
CDR(x, ...)

Arguments

x

otput of either MackChainLadder or BootChainLadder

dev

vector of development periods or "all". Currently only applicable for MackChainLadder output. Defines the years for which the run off claims development result should be returned.

probs

only applicable for BootChainLadder output. Define quantiles to be returned.

...

other arguments

Details

Merz & Wüthrich (2008) derived analytic formulae for the mean square error of prediction of the claims development result for the Mack chain-ladder model after one year assuming:

Value

A data.frame with various IBNR/reserves and one-year statistics of the claims development result.

Note

Tail factors are currently not supported.

Author(s)

Mario Wüthrich and Markus Gesmann with contributions from Arthur Charpentier and Arnaud Lacoume for CDR.MackChainLadder and Giuseppe Crupi and Markus Gesmann for CDR.BootChainLadder.

References

Michael Merz, Mario V. Wüthrich. Modelling the claims development result for solvency purposes. Casualty Actuarial Society E-Forum, Fall 2008.

Michael Merz, Mario V. Wüthrich. Claims Run-Off Uncertainty: The Full Picture. Swiss Finance Institute Research Paper No. 14-69. http://ssrn.com/abstract=2524352. 2014

See Also

See also MackChainLadder and BootChainLadder

Examples

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# Example from the 2008 Merz, Wuthrich paper mentioned above
MW2008
M <- MackChainLadder(MW2008, est.sigma="Mack")
plot(M)
CDR(M)
# Return all run-off result developments
CDR(M, dev="all")

# Example from the 2014 Merz, Wuthrich paper mentioned above
MW2014
W <- MackChainLadder(MW2014, est.sigma="Mack")
plot(W)
CDR(W)

# Example with the BootChainLadder function, assuming overdispered Poisson model
B <- BootChainLadder(MW2008, process.distr=c("od.pois"))
B
CDR(B)

Example output

Welcome to ChainLadder version 0.2.4

Type vignette('ChainLadder', package='ChainLadder') to access
the overall package documentation.

See demo(package='ChainLadder') for a list of demos.

More information is available on the ChainLadder project web-site:
https://github.com/mages/ChainLadder

To suppress this message use:
suppressPackageStartupMessages(library(ChainLadder))

      dev
origin       1       2       3       4       5       6       7       8       9
     1 2202584 3210449 3468122 3545070 3621627 3644636 3669012 3674511 3678633
     2 2350650 3553023 3783846 3840067 3865187 3878744 3898281 3902425      NA
     3 2321885 3424190 3700876 3798198 3854755 3878993 3898825      NA      NA
     4 2171487 3165274 3395841 3466453 3515703 3548422      NA      NA      NA
     5 2140328 3157079 3399262 3500520 3585812      NA      NA      NA      NA
     6 2290664 3338197 3550332 3641036      NA      NA      NA      NA      NA
     7 2148216 3219775 3428335      NA      NA      NA      NA      NA      NA
     8 2143728 3158581      NA      NA      NA      NA      NA      NA      NA
     9 2144738      NA      NA      NA      NA      NA      NA      NA      NA
             IBNR CDR(1)S.E.   Mack.S.E.
1           0.000     0.0000      0.0000
2        4377.670   566.1744    566.1744
3        9347.477  1486.5603   1563.8075
4       28392.406  3923.0986   4157.2733
5       51444.021  9722.8598  10536.4380
6      111811.123 28442.6216  30319.4638
7      187084.178 20954.2870  35967.0384
8      411864.225 28119.3180  45090.1821
9     1433505.008 53320.8210  69552.3397
Total 2237826.107 81080.5468 108401.3875
             IBNR CDR(1)S.E. CDR(2)S.E. CDR(3)S.E. CDR(4)S.E. CDR(5)S.E.
1           0.000     0.0000     0.0000     0.0000     0.0000     0.0000
2        4377.670   566.1744     0.0000     0.0000     0.0000     0.0000
3        9347.477  1486.5603   485.4195     0.0000     0.0000     0.0000
4       28392.406  3923.0986  1305.9869   431.9915     0.0000     0.0000
5       51444.021  9722.8598  3830.3960  1277.0783   423.8641     0.0000
6      111811.123 28442.6216  9689.5440  3820.5641  1274.3261   423.4215
7      187084.178 20954.2870 27423.5036  9340.4725  3684.4291  1229.1060
8      411864.225 28119.3180 20421.8007 26951.8084  9178.4040  3621.3651
9     1433505.008 53320.8210 27782.3071 20193.6339 26778.3919  9118.5624
Total 2237826.107 81080.5468 52222.0516 38517.4943 29104.1066 10109.0020
      CDR(6)S.E. CDR(7)S.E. CDR(8)S.E. CDR(9)S.E.   Mack.S.E.
1         0.0000     0.0000     0.0000          0      0.0000
2         0.0000     0.0000     0.0000          0    566.1744
3         0.0000     0.0000     0.0000          0   1563.8075
4         0.0000     0.0000     0.0000          0   4157.2733
5         0.0000     0.0000     0.0000          0  10536.4380
6         0.0000     0.0000     0.0000          0  30319.4638
7       408.6786     0.0000     0.0000          0  35967.0384
8      1208.1604   401.9014     0.0000          0  45090.1821
9      3598.2399  1200.5081   399.4584          0  69552.3397
Total  3876.0093  1281.3024   399.4584          0 108401.3875
      dev
origin     0     1     2     3     4     5     6     7     8     9    10    11
    1  13109 20355 21337 22043 22401 22658 22997 23158 23492 23664 23699 23904
    2  14457 22038 22627 23114 23238 23312 23440 23490 23964 23976 24048 24111
    3  16075 22672 23753 24052 24206 24757 24786 24807 24823 24888 24986 25401
    4  15682 23464 24465 25052 25529 25708 25752 25770 25835 26075 26082 26146
    5  16551 23706 24627 25573 26046 26115 26283 26481 26701 26718 26724 26728
    6  15439 23796 24866 25317 26139 26154 26175 26205 26764 26818 26836 26959
    7  14629 21645 22826 23599 24992 25434 25476 25549 25604 25709 25723    NA
    8  17585 26288 27623 27939 28335 28638 28715 28759 29525 30302    NA    NA
    9  17419 25941 27066 27761 28043 28477 28721 28878 28948    NA    NA    NA
    10 16665 25370 26909 27611 27729 27861 29830 29844    NA    NA    NA    NA
    11 15471 23745 25117 26378 26971 27396 27480    NA    NA    NA    NA    NA
    12 15103 23393 26809 27691 28061 29183    NA    NA    NA    NA    NA    NA
    13 14540 22642 23571 24127 24210    NA    NA    NA    NA    NA    NA    NA
    14 14590 22336 23440 24029    NA    NA    NA    NA    NA    NA    NA    NA
    15 13967 21515 22603    NA    NA    NA    NA    NA    NA    NA    NA    NA
    16 12930 20111    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
    17 12539    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
      dev
origin    12    13    14    15    16
    1  23960 23992 23994 24001 24002
    2  24252 24538 24540 24550    NA
    3  25681 25705 25732    NA    NA
    4  26150 26167    NA    NA    NA
    5  26735    NA    NA    NA    NA
    6     NA    NA    NA    NA    NA
    7     NA    NA    NA    NA    NA
    8     NA    NA    NA    NA    NA
    9     NA    NA    NA    NA    NA
    10    NA    NA    NA    NA    NA
    11    NA    NA    NA    NA    NA
    12    NA    NA    NA    NA    NA
    13    NA    NA    NA    NA    NA
    14    NA    NA    NA    NA    NA
    15    NA    NA    NA    NA    NA
    16    NA    NA    NA    NA    NA
    17    NA    NA    NA    NA    NA
              IBNR   CDR(1)S.E.    Mack.S.E.
1         0.000000    0.0000000    0.0000000
2         1.022874    0.4083149    0.4083149
3        10.085643    2.5393857    2.5652899
4        21.187574   16.7232632   16.8984949
5       117.662565  156.4022713  157.2756452
6       223.279748  137.6522771  207.1650862
7       361.808180  171.1812092  261.9266093
8       469.408830   70.3161155  292.2622285
9       653.504225  271.6352221  390.5874717
10     1008.763182  310.1268449  502.0606072
11     1011.859648  103.3834357  486.0911099
12     1406.702133  632.6388191  806.9028971
13     1492.903495  315.0489135  793.9381916
14     1917.636398  406.1424672  891.6613403
15     2458.152208  285.2076540  916.4940218
16     3384.341045  668.2337878 1106.1262716
17     9596.552341  733.2222786 1295.6909824
Total 24134.870088 1842.8507073 3233.6807352
BootChainLadder(Triangle = MW2008, process.distr = c("od.pois"))

     Latest Mean Ultimate Mean IBNR IBNR.S.E  IBNR 75%  IBNR 95%
1 3,678,633     3,678,633         0        0         0         0
2 3,902,425     3,906,888     4,463    5,841     6,950    15,072
3 3,898,825     3,908,342     9,517    7,695    13,490    24,168
4 3,548,422     3,576,964    28,542   12,004    36,184    49,763
5 3,585,812     3,636,507    50,695   15,447    61,900    77,848
6 3,641,036     3,752,650   111,614   22,604   125,038   151,719
7 3,428,335     3,616,611   188,276   30,344   208,032   242,343
8 3,158,581     3,571,270   412,689   43,002   442,126   485,346
9 2,144,738     3,579,143 1,434,405   97,427 1,501,006 1,600,955

                    Totals
Latest:         30,986,807
Mean Ultimate:  33,227,007
Mean IBNR:       2,240,200
IBNR.S.E           125,467
Total IBNR 75%:  2,317,280
Total IBNR 95%:  2,460,648
             IBNR   IBNR.S.E  CDR(1)S.E  CDR(1)75%  CDR(1)95%
1           0.000      0.000      0.000       0.00       0.00
2        4462.942   5841.260   5841.260    6949.50   15071.80
3        9516.851   7694.897   5711.646   12549.65   20397.88
4       28542.126  12004.446  10148.710   33929.41   47137.97
5       50695.080  15446.623  10269.697   57054.52   69350.69
6      111613.517  22603.606  17167.097  121701.78  142454.70
7      188275.709  30344.093  19306.714  199329.51  221911.30
8      412688.965  43001.608  32303.458  432822.46  467114.04
9     1434404.517  97426.714  89692.016 1496108.72 1577810.77
Total 2240199.706 125467.103 108576.859 2310378.79 2417946.98

ChainLadder documentation built on May 29, 2017, 2:08 p.m.