Compute everything belonging to the chosen special claims

This function computes every needed information about the chosen special claims in one step.

Usage

compute_special_claims(
  special_claims,
  extended_claims_data,
  first_orig_year,
  last_orig_year,
  end_of_tail,
  external_patterns = NULL,
  active_annuities = NULL,
  age_shift = NULL,
  mortality = NULL,
  reinsurance = NULL,
  indices = NULL
)

Arguments

special_claims: Dataframe with special claims, see details.
extended_claims_data: Prepared claims data dataframe, see details of prepare_data().
It is not necessary to reduce this dataframe to special claims, this will be done by the function.
first_orig_year: Integer value for the first origin year, will be treated as the first observed calendar year.
last_orig_year: Integer value for the last origin year which will also be treated as the last calendar year, usually the calendar year that just ended.
end_of_tail: Chosen development year of tail end.
external_patterns: List of external patterns that can be referred to in special_claims, see details. Default: NULL
Only necessary if special_claims$type is set to external.
active_annuities: Dataframe of active annuities, see active_annuities_xmpl. Default: NULL.
Only necessary if annuities shall be considered.
age_shift: Dataframe, see description of age_shift_xmpl. Default: NULL
Only necessary if annuities shall be considered.
mortality: Dataframe, see description of mortality_xmpl. Default: NULL
Only necessary if annuities shall be considered.
reinsurance: Dataframe with reinsurance information, see details of xl_cashflow() or reinsurance_xmpl. Default: NULL
Only necessary if reinsurance shall be considered.
indices: Dataframe for indexation, see details of prepare_data(). Default: NULL
Only necessary if reinsurance shall be considered.

Value

List of matrices. Each matrix consists of one row per year between first_orig_year and last_orig_year but the count of columns varies (with n be the number of origin years):

special_claims_payments with historic and future claim payments (250 + n columns)
special_claims_reserved with historic claims reserves (n columns)
special_annuities_payments with historic and future annuity payments (250 + n columns)
special_annuities_reserved with historic annuities reserves (n columns)
special_ceded_quota_payments with historic and future payments from the quota share reinsurance contract (250 + n columns)
special_ceded_xl_payments with historic and future payments from the xl reinsurance contract (250 + n columns)

Details

Some claims differ to historic claims so much that they cannot be reserved with the available pools. This mostly applies to very large claims that have not been observed yet hence there is no adequate historic data of similar claims in the pools. These claims must be separated and projected deterministically.

This package comes with some graphic options to identify special claims. After this process, the dataframe special_claims must be created with one row per special claim and the following columns:

Claim_id
type: character. Unique claim id.
Reserve2BE_percentage
type: numeric. This number will be multiplied with the latest claim reserve to calculate the best estimate reserve, e.g. 0.8 if 80% of the reserve will be needed for future payments.
Rollout_type
type: character. One of linear, constant or external.
- linear means that the payments will decrease evenly and reach 0 at end_of_tail. The sum is the desired best estimate.
- constant means equal payments until end_of_tail that add to the desired best estimate.
- external means that the best estimate is rolled out by an external pattern. The patterns must be specified in the list external_patterns. If external is chosen, the column Pattern_id is used.
Pattern_id type: integer. The number of the element of list external_patterns where the desired external pattern is specified.

The list external_patterns specifies the external patterns that special_claims$Pattern_id refers to. Hence this list must at least contain max(special_claims$Pattern_id) elements.
Each element is a numeric vector with future payments as a percentage of the best estimate reserve. Sum of vector must be 1.

Examples

# this example uses data provided with this package
extended_claims_data <- prepare_data(claims_data = minimal_claims_data_xmpl,
                                     indices = indices_xmpl,
                                     threshold = 400000,
                                     first_orig_year = 1989,
                                     last_orig_year = 2023,
                                     expected_year_of_growing_large = 3,
                                     reserve_classes = c(1, 200001, 400001, 700001, 1400001),
                                     pool_of_annuities = minimal_pool_of_annuities_xmpl)
# The claims with claim_ids Claim#43, Claim#44 and Claim#68 are identified as special claims.
special_claims <- data.frame(Claim_id = c("Claim#43", "Claim#44", "Claim#68"),
                             Reserve2BE_percentage = c(0.8, 0.5, 1.2),
                             Rollout_type = c("linear", "constant", "external"),
                             Pattern_id = c(1,1,3))
print(special_claims)
#>   Claim_id Reserve2BE_percentage Rollout_type Pattern_id
#> 1 Claim#43                   0.8       linear          1
#> 2 Claim#44                   0.5     constant          1
#> 3 Claim#68                   1.2     external          3

external_patterns <- list(c(0.5, 0.3, 0.2),
                          c(1),
                          c(0.7, 0.3))
print(external_patterns)
#> [[1]]
#> [1] 0.5 0.3 0.2
#> 
#> [[2]]
#> [1] 1
#> 
#> [[3]]
#> [1] 0.7 0.3
#> 

# First example ignores annuities and reinsurance.
result <- compute_special_claims(special_claims = special_claims,
                                 extended_claims_data = extended_claims_data,
                                 first_orig_year = 1989,
                                 last_orig_year = 2023,
                                 end_of_tail = 50,
                                 external_patterns = external_patterns)
print(str(result))
#> List of 6
#>  $ special_claims_payments     : num [1:35, 1:285] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:35] "1989" "1990" "1991" "1992" ...
#>   .. ..$ : chr [1:285] "1989" "1990" "1991" "1992" ...
#>  $ special_claims_reserved     : 'xtabs' num [1:35, 1:35] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ Origin_year  : chr [1:35] "1989" "1990" "1991" "1992" ...
#>   .. ..$ Calendar_year: chr [1:35] "1989" "1990" "1991" "1992" ...
#>   ..- attr(*, "call")= language xtabs(formula = substitute(i ~ j, list(i = as.name(col_name), j = quote(Origin_year +      Calendar_year))), data = data)
#>  $ special_annuities_payments  : num [1:35, 1:285] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:35] "1989" "1990" "1991" "1992" ...
#>   .. ..$ : chr [1:285] "1989" "1990" "1991" "1992" ...
#>  $ special_annuities_reserved  : 'xtabs' num [1:35, 1:35] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ Origin_year  : chr [1:35] "1989" "1990" "1991" "1992" ...
#>   .. ..$ Calendar_year: chr [1:35] "1989" "1990" "1991" "1992" ...
#>   ..- attr(*, "call")= language xtabs(formula = substitute(i ~ j, list(i = as.name(col_name), j = quote(Origin_year +      Calendar_year))), data = data)
#>  $ special_ceded_quota_payments: num [1:35, 1:285] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:35] "1989" "1990" "1991" "1992" ...
#>   .. ..$ : chr [1:285] "1989" "1990" "1991" "1992" ...
#>  $ special_ceded_xl_payments   : num [1:35, 1:285] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:35] "1989" "1990" "1991" "1992" ...
#>   .. ..$ : chr [1:285] "1989" "1990" "1991" "1992" ...
#> NULL
print(result$special_claims_payments[, c("2024", "2025", "2026", "2027", "2028", "2029")])
#>           2024      2025     2026     2027     2028    2029
#> 1989      0.00      0.00     0.00     0.00     0.00     0.0
#> 1990      0.00      0.00     0.00     0.00     0.00     0.0
#> 1991      0.00      0.00     0.00     0.00     0.00     0.0
#> 1992      0.00      0.00     0.00     0.00     0.00     0.0
#> 1993      0.00      0.00     0.00     0.00     0.00     0.0
#> 1994      0.00      0.00     0.00     0.00     0.00     0.0
#> 1995      0.00      0.00     0.00     0.00     0.00     0.0
#> 1996      0.00      0.00     0.00     0.00     0.00     0.0
#> 1997      0.00      0.00     0.00     0.00     0.00     0.0
#> 1998      0.00      0.00     0.00     0.00     0.00     0.0
#> 1999      0.00      0.00     0.00     0.00     0.00     0.0
#> 2000      0.00      0.00     0.00     0.00     0.00     0.0
#> 2001      0.00      0.00     0.00     0.00     0.00     0.0
#> 2002      0.00      0.00     0.00     0.00     0.00     0.0
#> 2003      0.00      0.00     0.00     0.00     0.00     0.0
#> 2004      0.00      0.00     0.00     0.00     0.00     0.0
#> 2005      0.00      0.00     0.00     0.00     0.00     0.0
#> 2006  19094.48  18752.05 18409.61 18067.17 17724.73 17382.3
#> 2007      0.00      0.00     0.00     0.00     0.00     0.0
#> 2008      0.00      0.00     0.00     0.00     0.00     0.0
#> 2009      0.00      0.00     0.00     0.00     0.00     0.0
#> 2010      0.00      0.00     0.00     0.00     0.00     0.0
#> 2011      0.00      0.00     0.00     0.00     0.00     0.0
#> 2012      0.00      0.00     0.00     0.00     0.00     0.0
#> 2013      0.00      0.00     0.00     0.00     0.00     0.0
#> 2014      0.00      0.00     0.00     0.00     0.00     0.0
#> 2015      0.00      0.00     0.00     0.00     0.00     0.0
#> 2016      0.00      0.00     0.00     0.00     0.00     0.0
#> 2017      0.00      0.00     0.00     0.00     0.00     0.0
#> 2018      0.00      0.00     0.00     0.00     0.00     0.0
#> 2019 242822.29 104066.70     0.00     0.00     0.00     0.0
#> 2020      0.00      0.00     0.00     0.00     0.00     0.0
#> 2021      0.00      0.00     0.00     0.00     0.00     0.0
#> 2022      0.00      0.00     0.00     0.00     0.00     0.0
#> 2023      0.00      0.00     0.00     0.00     0.00     0.0

# Second example also computes annuities for claim#43
result <- compute_special_claims(special_claims = special_claims,
                                 extended_claims_data = extended_claims_data,
                                 first_orig_year = 1989,
                                 last_orig_year = 2023,
                                 end_of_tail = 50,
                                 external_patterns = external_patterns,
                                 active_annuities = minimal_active_annuities_xmpl,
                                 age_shift = age_shift_xmpl,
                                 mortality = mortality_xmpl)
print(result$special_annuities_payments[, c("2024", "2025", "2026", "2027", "2028", "2029")])
#>          2024     2025     2026     2027     2028     2029
#> 1989     0.00    0.000    0.000    0.000    0.000    0.000
#> 1990     0.00    0.000    0.000    0.000    0.000    0.000
#> 1991     0.00    0.000    0.000    0.000    0.000    0.000
#> 1992     0.00    0.000    0.000    0.000    0.000    0.000
#> 1993     0.00    0.000    0.000    0.000    0.000    0.000
#> 1994     0.00    0.000    0.000    0.000    0.000    0.000
#> 1995     0.00    0.000    0.000    0.000    0.000    0.000
#> 1996     0.00    0.000    0.000    0.000    0.000    0.000
#> 1997     0.00    0.000    0.000    0.000    0.000    0.000
#> 1998     0.00    0.000    0.000    0.000    0.000    0.000
#> 1999     0.00    0.000    0.000    0.000    0.000    0.000
#> 2000     0.00    0.000    0.000    0.000    0.000    0.000
#> 2001     0.00    0.000    0.000    0.000    0.000    0.000
#> 2002     0.00    0.000    0.000    0.000    0.000    0.000
#> 2003     0.00    0.000    0.000    0.000    0.000    0.000
#> 2004     0.00    0.000    0.000    0.000    0.000    0.000
#> 2005     0.00    0.000    0.000    0.000    0.000    0.000
#> 2006 12168.21 8678.269 6160.377 4352.512 3060.705 2142.111
#> 2007     0.00    0.000    0.000    0.000    0.000    0.000
#> 2008     0.00    0.000    0.000    0.000    0.000    0.000
#> 2009     0.00    0.000    0.000    0.000    0.000    0.000
#> 2010     0.00    0.000    0.000    0.000    0.000    0.000
#> 2011     0.00    0.000    0.000    0.000    0.000    0.000
#> 2012     0.00    0.000    0.000    0.000    0.000    0.000
#> 2013     0.00    0.000    0.000    0.000    0.000    0.000
#> 2014     0.00    0.000    0.000    0.000    0.000    0.000
#> 2015     0.00    0.000    0.000    0.000    0.000    0.000
#> 2016     0.00    0.000    0.000    0.000    0.000    0.000
#> 2017     0.00    0.000    0.000    0.000    0.000    0.000
#> 2018     0.00    0.000    0.000    0.000    0.000    0.000
#> 2019     0.00    0.000    0.000    0.000    0.000    0.000
#> 2020     0.00    0.000    0.000    0.000    0.000    0.000
#> 2021     0.00    0.000    0.000    0.000    0.000    0.000
#> 2022     0.00    0.000    0.000    0.000    0.000    0.000
#> 2023     0.00    0.000    0.000    0.000    0.000    0.000

# Third example also computes reinsurance
# Priority in 2019 is set to 100.000 to produce a positive xl portion
reinsurance_xmpl[reinsurance_xmpl$Origin_year == 2019, "Priority"] <- 100000

result <- compute_special_claims(special_claims = special_claims,
                                 extended_claims_data = extended_claims_data,
                                 first_orig_year = 1989,
                                 last_orig_year = 2023,
                                 end_of_tail = 50,
                                 external_patterns = external_patterns,
                                 active_annuities = minimal_active_annuities_xmpl,
                                 age_shift = age_shift_xmpl,
                                 mortality = mortality_xmpl,
                                 reinsurance = reinsurance_xmpl,
                                 indices = indices_xmpl)
print(result$special_ceded_xl_payments[, c("2024", "2025", "2026", "2027", "2028", "2029")])
#>          2024     2025 2026 2027 2028 2029
#> 1989      0.0     0.00    0    0    0    0
#> 1990      0.0     0.00    0    0    0    0
#> 1991      0.0     0.00    0    0    0    0
#> 1992      0.0     0.00    0    0    0    0
#> 1993      0.0     0.00    0    0    0    0
#> 1994      0.0     0.00    0    0    0    0
#> 1995      0.0     0.00    0    0    0    0
#> 1996      0.0     0.00    0    0    0    0
#> 1997      0.0     0.00    0    0    0    0
#> 1998      0.0     0.00    0    0    0    0
#> 1999      0.0     0.00    0    0    0    0
#> 2000      0.0     0.00    0    0    0    0
#> 2001      0.0     0.00    0    0    0    0
#> 2002      0.0     0.00    0    0    0    0
#> 2003      0.0     0.00    0    0    0    0
#> 2004      0.0     0.00    0    0    0    0
#> 2005      0.0     0.00    0    0    0    0
#> 2006      0.0     0.00    0    0    0    0
#> 2007      0.0     0.00    0    0    0    0
#> 2008      0.0     0.00    0    0    0    0
#> 2009      0.0     0.00    0    0    0    0
#> 2010      0.0     0.00    0    0    0    0
#> 2011      0.0     0.00    0    0    0    0
#> 2012      0.0     0.00    0    0    0    0
#> 2013      0.0     0.00    0    0    0    0
#> 2014      0.0     0.00    0    0    0    0
#> 2015      0.0     0.00    0    0    0    0
#> 2016      0.0     0.00    0    0    0    0
#> 2017      0.0     0.00    0    0    0    0
#> 2018      0.0     0.00    0    0    0    0
#> 2019 193753.2 82762.24    0    0    0    0
#> 2020      0.0     0.00    0    0    0    0
#> 2021      0.0     0.00    0    0    0    0
#> 2022      0.0     0.00    0    0    0    0
#> 2023      0.0     0.00    0    0    0    0
print(result$special_ceded_quota_payments[, c("2024", "2025", "2026", "2027", "2028", "2029")])
#>           2024      2025     2026     2027     2028     2029
#> 1989     0.000     0.000    0.000    0.000    0.000    0.000
#> 1990     0.000     0.000    0.000    0.000    0.000    0.000
#> 1991     0.000     0.000    0.000    0.000    0.000    0.000
#> 1992     0.000     0.000    0.000    0.000    0.000    0.000
#> 1993     0.000     0.000    0.000    0.000    0.000    0.000
#> 1994     0.000     0.000    0.000    0.000    0.000    0.000
#> 1995     0.000     0.000    0.000    0.000    0.000    0.000
#> 1996     0.000     0.000    0.000    0.000    0.000    0.000
#> 1997     0.000     0.000    0.000    0.000    0.000    0.000
#> 1998     0.000     0.000    0.000    0.000    0.000    0.000
#> 1999     0.000     0.000    0.000    0.000    0.000    0.000
#> 2000     0.000     0.000    0.000    0.000    0.000    0.000
#> 2001     0.000     0.000    0.000    0.000    0.000    0.000
#> 2002     0.000     0.000    0.000    0.000    0.000    0.000
#> 2003     0.000     0.000    0.000    0.000    0.000    0.000
#> 2004     0.000     0.000    0.000    0.000    0.000    0.000
#> 2005     0.000     0.000    0.000    0.000    0.000    0.000
#> 2006  9378.809  8229.095 7370.996 6725.905 6235.632 5857.322
#> 2007     0.000     0.000    0.000    0.000    0.000    0.000
#> 2008     0.000     0.000    0.000    0.000    0.000    0.000
#> 2009     0.000     0.000    0.000    0.000    0.000    0.000
#> 2010     0.000     0.000    0.000    0.000    0.000    0.000
#> 2011     0.000     0.000    0.000    0.000    0.000    0.000
#> 2012     0.000     0.000    0.000    0.000    0.000    0.000
#> 2013     0.000     0.000    0.000    0.000    0.000    0.000
#> 2014     0.000     0.000    0.000    0.000    0.000    0.000
#> 2015     0.000     0.000    0.000    0.000    0.000    0.000
#> 2016     0.000     0.000    0.000    0.000    0.000    0.000
#> 2017     0.000     0.000    0.000    0.000    0.000    0.000
#> 2018     0.000     0.000    0.000    0.000    0.000    0.000
#> 2019 48564.459 20813.339    0.000    0.000    0.000    0.000
#> 2020     0.000     0.000    0.000    0.000    0.000    0.000
#> 2021     0.000     0.000    0.000    0.000    0.000    0.000
#> 2022     0.000     0.000    0.000    0.000    0.000    0.000
#> 2023     0.000     0.000    0.000    0.000    0.000    0.000