Parallel Based Development Profile Reserve

The function takes a cumulative (or incremental) run-off triangle (partially or completely observed) and returns the reserve prediction obtained by the PARALLAX or REACT algorithm (see Maciak, Mizera, and Pešta (2022) for more details). If a full data matrix is provided as the input then the algorithms uses only on the relevant part of the data—the run-off triangle only (i.e., the top-left triangular part of the matrix) but standard incremental residuals (true incremental payments minus predicted increments) are returned for retrospective validation purposes (if residuals = TRUE). If the run-off triangle is provided only,then the algorithm caclulates so-called back-fitted (incremental) residuals instead (see Maciak, Mizera, and Pešta (2022) for details).

Usage

parallelReserve(
  chainLadder,
  method = "parallax",
  cum = TRUE,
  residuals = FALSE
)

Arguments

chainLadder: cumulative or incremental run-off triangle (the triangle must be of the class triangle or matrix) in terms of a square matrix (i.e., a fully observed run-off triangle) or a standard run-off triangle instead (i.e, the top-left triangular part of the matrix
method: prediction method to be used: PARALLAX (DEFAULT method = "parallax") or REACT (method = "react")
cum: logical (TRUE for a cumulative triangle and FALSE for an incremental triangle)
residuals: logical to indicate whether incremental residuals should be provided or not. If the run-off triangle is complete then the residuals are obtained in terms of true increments minus the predicted increments. If the bottom-right part of the triangle is not available the residuals are provided in terms of the backfitting approach (see Maciak, Mizera, and Pesta (2022) for further details)

Value

An object of the class profileLadder which is a list with the following elements:

reserve: numeric vector with four values summarizing the reserve: Total paid amount (i.e., the sum of the last observed diagonal in a cumulative run-off triangle); Total estimated amount (i.e., the sum of the last column in the completed cumulative triangle); Estimated reserve (i.e., the sum of the last column in the completed cumulative triangle minus the sum of the last observed diagonal in chainLadder); True reserve—if the completed (true) chainLadder is provided in the input (i.e., the sum of the last column in chainLadder minus the sum of the last diagonal in chainLadder)
method: algorithm used for the reserve estimation (PARALLAX or REACT)
Triangle: the run-off triangle considered as the input for the underlying estimation algorithm (PARALLAX or REACT)
FullTriangle: completed functional development profiles (the lower-right triangular part in completed) estimated by the PARALLAX algorithm or the REACT algorithm
trueCompleted: true (complete) run-off triangle (if available) and NA value provided otherwise
residuals: a triangle with the corresponding residuals (for residuals = TRUE). The residuals are either provided in the upper-left triangle (so-called back-fitted incremental residuals if true completed triangle is not available) or the residuals are given in the lower-right triangle (i,e., standard incremental residuals—if the true completed triangle is given)

References

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4

Examples

## run-off (upper-left) triangle with NA values (bottom-right part)
data(MW2014, package = "ChainLadder")
print(MW2014) 
#>       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
parallelReserve(MW2014, residuals = TRUE)
#> PARALLAX Reserving 
#>     Estimated Reserve    Estimated Ultimate           Paid Amount 
#>                 25385                454502                429117 
#>          True Reserve 
#>                    NA 
#> 
#> PARALLAX method (functional profile completion)
#> 13109 	20355 	21337 	22043 	22401 	22658 	22997 	23158 	23492 	23664 	23699 	23904 	23960 	23992 	23994 	24001 	24002 	
#> 14457 	22038 	22627 	23114 	23238 	23312 	23440 	23490 	23964 	23976 	24048 	24111 	24252 	24538 	24540 	24550 	24551 	
#> 16075 	22672 	23753 	24052 	24206 	24757 	24786 	24807 	24823 	24888 	24986 	25401 	25681 	25705 	25732 	25742 	25743 	
#> 15682 	23464 	24465 	25052 	25529 	25708 	25752 	25770 	25835 	26075 	26082 	26146 	26150 	26167 	26194 	26204 	26205 	
#> 16551 	23706 	24627 	25573 	26046 	26115 	26283 	26481 	26701 	26718 	26724 	26728 	26735 	26752 	26779 	26789 	26790 	
#> 15439 	23796 	24866 	25317 	26139 	26154 	26175 	26205 	26764 	26818 	26836 	26959 	26966 	26983 	27010 	27020 	27021 	
#> 14629 	21645 	22826 	23599 	24992 	25434 	25476 	25549 	25604 	25709 	25723 	25787 	25791 	25815 	25842 	25852 	25853 	
#> 17585 	26288 	27623 	27939 	28335 	28638 	28715 	28759 	29525 	30302 	30320 	30443 	30450 	30467 	30494 	30504 	30505 	
#> 17419 	25941 	27066 	27761 	28043 	28477 	28721 	28878 	28948 	29725 	29743 	29866 	29873 	29890 	29917 	29927 	29928 	
#> 16665 	25370 	26909 	27611 	27729 	27861 	29830 	29844 	29914 	30691 	30709 	30832 	30839 	30856 	30883 	30893 	30894 	
#> 15471 	23745 	25117 	26378 	26971 	27396 	27480 	27678 	28444 	29221 	29239 	29362 	29369 	29386 	29413 	29423 	29424 	
#> 15103 	23393 	26809 	27691 	28061 	29183 	29260 	29417 	29487 	30264 	30282 	30405 	30412 	30429 	30456 	30466 	30467 	
#> 14540 	22642 	23571 	24127 	24210 	24761 	24790 	24811 	24827 	24892 	24990 	25405 	25685 	25709 	25736 	25746 	25747 	
#> 14590 	22336 	23440 	24029 	24183 	24734 	24763 	24784 	24800 	24865 	24963 	25378 	25658 	25682 	25709 	25719 	25720 	
#> 13967 	21515 	22603 	23090 	23214 	23288 	23416 	23466 	23940 	23952 	24024 	24087 	24228 	24514 	24516 	24526 	24527 	
#> 12930 	20111 	21093 	21799 	22157 	22414 	22753 	22914 	23248 	23420 	23455 	23660 	23716 	23748 	23750 	23757 	23758 	
#> 12539 	19720 	20702 	21408 	21766 	22023 	22362 	22523 	22857 	23029 	23064 	23269 	23325 	23357 	23359 	23366 	23367 	

## completed run-off triangle with 'unknown' truth (lower-bottom part)  
## for the estimation purposes only the upper-left triangle is used 
data(CameronMutual)
parallelReserve(CameronMutual, residuals = TRUE)
#> PARALLAX Reserving 
#>     Estimated Reserve    Estimated Ultimate           Paid Amount 
#>                  8540                113699                105159 
#>          True Reserve 
#>                  7963 
#> 
#> PARALLAX method (functional profile completion)
#> 5244 	 9228 	10823 	11352 	11791 	12082 	12120 	12199 	12215 	12215 	
#> 5984 	 9939 	11725 	12346 	12746 	12909 	13034 	13109 	13113 	13113 	
#> 7452 	12421 	14171 	14752 	15066 	15354 	15637 	15720 	15724 	15724 	
#> 7115 	11117 	12488 	13274 	13662 	13859 	13872 	13947 	13951 	13951 	
#> 5753 	 8969 	 9917 	10697 	11135 	11282 	11320 	11399 	11415 	11415 	
#> 3937 	 6524 	 7989 	 8543 	 8757 	 8904 	 8942 	 9021 	 9037 	 9037 	
#> 5127 	 8212 	 8976 	 9325 	 9539 	 9686 	 9724 	 9803 	 9819 	 9819 	
#> 5046 	 8006 	 8984 	 9333 	 9547 	 9694 	 9732 	 9811 	 9827 	 9827 	
#> 5129 	 8202 	 8966 	 9315 	 9529 	 9676 	 9714 	 9793 	 9809 	 9809 	
#> 3689 	 6276 	 7741 	 8295 	 8509 	 8656 	 8694 	 8773 	 8789 	 8789 	

## the previous output is identical (in term of the reserve prediction) 
## but back-fitted residuals are provided in the output instead 
print(observed(CameronMutual))
#>       dev
#> origin    1     2     3     4     5     6     7     8     9    10
#>     1  5244  9228 10823 11352 11791 12082 12120 12199 12215 12215
#>     2  5984  9939 11725 12346 12746 12909 13034 13109 13113    NA
#>     3  7452 12421 14171 14752 15066 15354 15637 15720    NA    NA
#>     4  7115 11117 12488 13274 13662 13859 13872    NA    NA    NA
#>     5  5753  8969  9917 10697 11135 11282    NA    NA    NA    NA
#>     6  3937  6524  7989  8543  8757    NA    NA    NA    NA    NA
#>     7  5127  8212  8976  9325    NA    NA    NA    NA    NA    NA
#>     8  5046  8006  8984    NA    NA    NA    NA    NA    NA    NA
#>     9  5129  8202    NA    NA    NA    NA    NA    NA    NA    NA
#>     10 3689    NA    NA    NA    NA    NA    NA    NA    NA    NA
parallelReserve(observed(CameronMutual), residuals = TRUE)
#> PARALLAX Reserving 
#>     Estimated Reserve    Estimated Ultimate           Paid Amount 
#>                  8540                113699                105159 
#>          True Reserve 
#>                    NA 
#> 
#> PARALLAX method (functional profile completion)
#> 5244 	 9228 	10823 	11352 	11791 	12082 	12120 	12199 	12215 	12215 	
#> 5984 	 9939 	11725 	12346 	12746 	12909 	13034 	13109 	13113 	13113 	
#> 7452 	12421 	14171 	14752 	15066 	15354 	15637 	15720 	15724 	15724 	
#> 7115 	11117 	12488 	13274 	13662 	13859 	13872 	13947 	13951 	13951 	
#> 5753 	 8969 	 9917 	10697 	11135 	11282 	11320 	11399 	11415 	11415 	
#> 3937 	 6524 	 7989 	 8543 	 8757 	 8904 	 8942 	 9021 	 9037 	 9037 	
#> 5127 	 8212 	 8976 	 9325 	 9539 	 9686 	 9724 	 9803 	 9819 	 9819 	
#> 5046 	 8006 	 8984 	 9333 	 9547 	 9694 	 9732 	 9811 	 9827 	 9827 	
#> 5129 	 8202 	 8966 	 9315 	 9529 	 9676 	 9714 	 9793 	 9809 	 9809 	
#> 3689 	 6276 	 7741 	 8295 	 8509 	 8656 	 8694 	 8773 	 8789 	 8789

Usage

Arguments

Value

References

See also

Examples