Rolling out one or more annuities
roll_out_annuity.RdRolling out one or more annuities
Arguments
- payments
numeric vector or matrix of agreed future payments with one row per annuity and 130 columns for future payments.
- probs
numeric vector or matrix with to
paymentscorresponding mortality probabilities. Must be of same size aspayments.- stop.at
Chose between
random_death_year(stochastic approach) andend_of_probs(deterministic approach). The first samples a random death year of the annuity recipient and returns the agreed payments up to that year and 0 after. The latter multiplies the payments with the corresponding mortality probabilities and returns a best estimate payment per year.
Examples
# this example uses data provided with this package
print(minimal_active_annuities_xmpl)
#> Claim_id Annuity_id Origin_year Calendar_year Entering_year Annuity_start
#> 1 Claim#43 1 2006 2023 2009 2009
#> 2 Claim#51 1 2010 2023 2013 2036
#> 3 Claim#13 1 1990 2023 1992 1992
#> Annuity_end Birth_year Gender Annual_payment Dynamic
#> 1 0 1939 m 12168.21 0
#> 2 2051 1986 m 12893.00 0
#> 3 0 1958 w 11807.36 0
# Create payments matrix
payments <- generate_annuity_payments(annuities = minimal_active_annuities_xmpl,
last_orig_year = 2023)
print(payments[,1:10])
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 12168.21 12168.21 12168.21 12168.21 12168.21 12168.21 12168.21 12168.21
#> [2,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
#> [3,] 11807.36 11807.36 11807.36 11807.36 11807.36 11807.36 11807.36 11807.36
#> [,9] [,10]
#> [1,] 12168.21 12168.21
#> [2,] 0.00 0.00
#> [3,] 11807.36 11807.36
# Create probability matrix
probs <- generate_annuity_probabilities(annuities = minimal_active_annuities_xmpl,
mortality = mortality_xmpl,
age_shift = age_shift_xmpl)
print(probs[,1:10])
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 0.2868083 0.4937320 0.6423048 0.7484672 0.8239585 0.8773790 0.9149971
#> [2,] 0 0.1136917 0.2174082 0.3115931 0.3967347 0.4733544 0.5419961 0.6032160
#> [3,] 0 0.1839400 0.3364235 0.4623482 0.5659430 0.6508416 0.7201519 0.7765189
#> [,9] [,10]
#> [1,] 0.9413576 0.9597385
#> [2,] 0.6575737 0.7056247
#> [3,] 0.8221835 0.8590354
# stochastic with random death year
roll_out_annuity(payments, probs, stop.at = "random_death_year")
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 12168.21 12168.21 0 0 0 0 0 0 0 0 0 0
#> [2,] 0.00 0.00 0 0 0 0 0 0 0 0 0 0
#> [3,] 11807.36 0.00 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,49] [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,61] [,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,73] [,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,85] [,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,97] [,98] [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0
#> [,108] [,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117]
#> [1,] 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0
#> [,118] [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127]
#> [1,] 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0
#> [,128] [,129] [,130]
#> [1,] 0 0 0
#> [2,] 0 0 0
#> [3,] 0 0 0
# deterministic multiplying with mortality probabilities
roll_out_annuity(payments, probs, stop.at = "end_of_probs")
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 12168.21 8678.269 6160.377 4352.512 3060.705 2142.111 1492.078 1034.334
#> [2,] 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> [3,] 11807.36 9635.513 7835.086 6348.247 5125.067 4122.638 3304.267 2638.722
#> [,9] [,10] [,11] [,12] [,13] [,14] [,15]
#> [1,] 713.5738 489.91 334.7208 227.5767 153.9717 103.6602 69.44326
#> [2,] 0.0000 0.00 0.0000 0.0000 2355.7066 1993.7719 1680.80789
#> [3,] 2099.5428 1664.42 1314.6251 1034.5136 811.0724 633.5287 493.00357
#> [,16] [,17] [,18] [,19] [,20] [,21] [,22]
#> [1,] 46.28972 30.70185 20.26092 13.30323 8.690559 5.64832 3.652251
#> [2,] 1411.37438 1180.43237 983.34935 815.89725 674.243886 554.93924 454.897568
#> [3,] 382.21252 295.20566 227.14501 174.11422 132.957104 101.14136 76.644245
#> [,23] [,24] [,25] [,26] [,27] [,28]
#> [1,] 2.349417 1.503509 0.9571654 0.6061649 0.3818611 0.2392869
#> [2,] 371.376479 301.953836 244.5033443 197.1695344 158.3427454 126.6346106
#> [3,] 57.857208 43.506691 32.5888323 24.3158313 18.0721743 13.3790716
#> [,29] [,30] [,31] [,32] [,33] [,34]
#> [1,] 0.1491485 0.09246836 0.05702023 0.03497146 0.02133215 0.01294133
#> [2,] 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [3,] 9.8657274 7.24624521 5.30115976 3.86274307 2.80337291 2.02637138
#> [,35] [,36] [,37] [,38] [,39] [,40] [,41]
#> [1,] 0.007807881 0.004684728 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
#> [2,] 0.000000000 0.000000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
#> [3,] 1.458825287 1.045987456 0.7469327 0.5312036 0.3762338 0.2653778 0.186412
#> [,42] [,43] [,44] [,45] [,46] [,47] [,48]
#> [1,] 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000
#> [2,] 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000
#> [3,] 0.1304001 0.09083847 0.06301465 0.04352968 0.0299429 0.02050969 0.01398857
#> [,49] [,50] [,51] [,52] [,53] [,54]
#> [1,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
#> [2,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
#> [3,] 0.009500102 0.006424159 0.004325429 0.002899739 0.001935518 0.001286281
#> [,55] [,56] [,57] [,58] [,59] [,60]
#> [1,] 0.0000000000 0.000000000 0.0000000000 0.0000000000 0.0000000000 0
#> [2,] 0.0000000000 0.000000000 0.0000000000 0.0000000000 0.0000000000 0
#> [3,] 0.0008510718 0.000560635 0.0003676794 0.0002400628 0.0001560408 0
#> [,61] [,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,73] [,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,85] [,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [,97] [,98] [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0
#> [,108] [,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117]
#> [1,] 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0
#> [,118] [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127]
#> [1,] 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0
#> [,128] [,129] [,130]
#> [1,] 0 0 0
#> [2,] 0 0 0
#> [3,] 0 0 0