Actuarial
actu chain_ladderactu chain_ladderactu bfactu bfactu life_tableactu life_tableactu annuityactu annuityactu insuranceactu insuranceactu pure_premiumactu pure_premiumactu credibilityactu credibility
actu chain_ladder <json_triangle>
Description
Chain ladder on a cumulative triangle: development factors, ultimates, reserves by origin, Mack standard errors and total reserve with its interval
Chain ladder on a cumulative triangle: development factors, ultimates, reserves by origin, Mack standard errors and total reserve with its interval
Parameters
json_triangle: The cumulative triangle - String - required
json_triangle: The cumulative triangle - String - required
admin
actu chain_ladder "[[1000, 1800, 2100, 2200], [1100, 2000, 2350, null], [1250, 2200, null, null], [1300, null, null, null]]"
mentdb
{"factors": [1.791044776119403, 1.1710526315789473, 1.0476190476190477], "cumulative_factors": [2.1972842554146563, 1.2268170426065164, 1.0476190476190477, 1], "sigma2": [1.047489823609225, 0.06578947368421006, 0.004132025677091505], "origins": [{"origin": 0, "latest": 2200, "ultimate": 2200, "reserve": 0, "mack_se": 0, "cv": 0}, {"origin": 1, "latest": 2350, "ultimate": 2461.904761904762, "reserve": 111.90476190476193, "mack_se": 4.536133161215431, "cv": 0.0405356580363932}, {"origin": 2, "latest": 2200, "ultimate": 2698.997493734336, "reserve": 498.9974937343359, "mack_se": 16.56865632019587, "cv": 0.03320388684961402}, {"origin": 3, "latest": 1300, "ultimate": 2856.469532039053, "reserve": 1556.4695320390529, "mack_se": 56.05249715226347, "cv": 0.03601258874552584}], "total_reserve": 2167.3717876781507, "total_mack_se": 60.89603045964684, "total_cv": 0.028096716403641656, "lower": 2048.0177611757886, "upper": 2286.7258141805128, "tail": 1, "projected": [[1000, 1800, 2100, 2200], [1100, 2000, 2350, 2461.904761904762], [1250, 2200, 2576.315789473684, 2698.997493734336], [1300, 2328.3582089552237, 2726.6300078554596, 2856.469532039053]]}
Complete: reserves -> totals in thousands
admin
json load "tuto_c" (actu chain_ladder "[[357848, 766940, 610542, 482940, 527326, 574398, 146342, 139950, 227229, 67948], [352118, 884021, 933894, 1183289, 445745, 320996, 527804, 266172, 425046], [290507, 1001799, 926219, 1016654, 750816, 146923, 495992, 280405], [310608, 1108250, 776189, 1562400, 272482, 352053, 206286], [443160, 693190, 991983, 769488, 504851, 470639], [396132, 937085, 847498, 805037, 705960], [440832, 847631, 1131398, 1063269], [359480, 1061648, 1443370], [376686, 986608], [344014]]" "{\"incremental\": true}"); -> "[res]" (concat "reserve " (math round (/ (json select "tuto_c" "/total_reserve") 1000) 0) " k, Mack se " (math round (/ (json select "tuto_c" "/total_mack_se") 1000) 0) " k"); json unload "tuto_c"; [res]
mentdb
reserve 18681 k, Mack se 2447 k
actu chain_ladder <json_triangle> <json_params>
Description
Chain ladder with parameters: incremental (the triangle gives the payments of each year), tail (tail factor), level
Chain ladder with parameters: incremental (the triangle gives the payments of each year), tail (tail factor), level
Parameters
json_triangle: The triangle - String - required
json_params: The parameters - String - required
json_triangle: The triangle - String - required
json_params: The parameters - String - required
admin
actu chain_ladder "[[357848, 766940, 610542, 482940, 527326, 574398, 146342, 139950, 227229, 67948], [352118, 884021, 933894, 1183289, 445745, 320996, 527804, 266172, 425046], [290507, 1001799, 926219, 1016654, 750816, 146923, 495992, 280405], [310608, 1108250, 776189, 1562400, 272482, 352053, 206286], [443160, 693190, 991983, 769488, 504851, 470639], [396132, 937085, 847498, 805037, 705960], [440832, 847631, 1131398, 1063269], [359480, 1061648, 1443370], [376686, 986608], [344014]]" "{\"incremental\": true}"
mentdb
{"factors": [3.4906065479322863, 1.7473326421004893, 1.4574128360182361, 1.1738517093997867, 1.103823532244344, 1.0862693644363943, 1.0538743555048127, 1.0765551783529383, 1.017724725219544], "cumulative_factors": [14.4465768672924, 4.138701016260354, 2.3685822129924685, 1.6251964813646196, 1.3844989689503577, 1.2542756414472627, 1.1546635507833156, 1.0956368230729214, 1.017724725219544, 1], "sigma2": [160280.32748048689, 37736.85504799638, 41965.21301742404, 15182.902680976436, 13731.323891978891, 8185.771620009633, 446.616550105352, 1147.3659684286617, 446.616550105352], "origins": [{"origin": 0, "latest": 3901463, "ultimate": 3901463, "reserve": 0, "mack_se": 0, "cv": 0}, {"origin": 1, "latest": 5339085, "ultimate": 5433718.8145487895, "reserve": 94633.81454878952, "mack_se": 75535.04075748839, "cv": 0.7981823528686509}, {"origin": 2, "latest": 4909315, "ultimate": 5378826.29006424, "reserve": 469511.2900642399, "mack_se": 121698.56164542341, "cv": 0.2592026309500934}, {"origin": 3, "latest": 4588268, "ultimate": 5297905.820825461, "reserve": 709637.8208254613, "mack_se": 133548.85301207833, "cv": 0.18819297547688807}, {"origin": 4, "latest": 3873311, "ultimate": 4858199.639049737, "reserve": 984888.6390497368, "mack_se": 261406.44934268505, "cv": 0.2654172654432295}, {"origin": 5, "latest": 3691712, "ultimate": 5111171.457661661, "reserve": 1419459.4576616613, "mack_se": 411009.70388105325, "cv": 0.2895536759874268}, {"origin": 6, "latest": 3483130, "ultimate": 5660770.620135546, "reserve": 2177640.6201355457, "mack_se": 558316.8580711902, "cv": 0.2563861331886977}, {"origin": 7, "latest": 2864498, "ultimate": 6784799.011952501, "reserve": 3920301.011952501, "mack_se": 875327.5119113593, "cv": 0.22328068922325012}, {"origin": 8, "latest": 1363294, "ultimate": 5642266.263261642, "reserve": 4278972.263261642, "mack_se": 971257.8064699426, "cv": 0.22698389863588464}, {"origin": 9, "latest": 344014, "ultimate": 4969824.694424726, "reserve": 4625810.694424726, "mack_se": 1363154.911732307, "cv": 0.29468454326833005}], "total_reserve": 1.8680855611924306E7, "total_mack_se": 2447094.8608346656, "total_cv": 0.13099479550993604, "lower": 1.3884637817935307E7, "upper": 2.3477073405913305E7, "tail": 1, "projected": [[357848, 1124788, 1735330, 2218270, 2745596, 3319994, 3466336, 3606286, 3833515, 3901463], [352118, 1236139, 2170033, 3353322, 3799067, 4120063, 4647867, 4914039, 5339085, 5433718.8145487895], [290507, 1292306, 2218525, 3235179, 3985995, 4132918, 4628910, 4909315, 5285148.485415756, 5378826.29006424], [310608, 1418858, 2195047, 3757447, 4029929, 4381982, 4588268, 4835457.981383356, 5205637.329566298, 5297905.820825461], [443160, 1136350, 2128333, 2897821, 3402672, 3873311, 4207459.078234495, 4434133.224387251, 4773589.084220907, 4858199.639049737], [396132, 1333217, 2180715, 2985752, 3691712, 4074998.579868831, 4426546.117433324, 4665023.436622376, 5022155.137833639, 5111171.457661661], [440832, 1288463, 2419861, 3483130, 4088678.104561679, 4513179.107587381, 4902528.200786558, 5166648.747948103, 5562182.464334255, 5660770.620135546], [359480, 1421128, 2864498, 4174756.1539485655, 4900544.647639803, 5409336.502878881, 5875996.52500483, 6192562.0507379845, 6666634.742993869, 6784799.011952501], [376686, 1363294, 2382128.1069797445, 3471744.080152102, 4075312.7230851348, 4498426.084996149, 4886502.444312864, 5149759.614172911, 5544000.379910678, 5642266.263261642], [344014, 1200817.5209803774, 2098227.651615203, 3057983.912352396, 3589619.6428319076, 3962306.6335643963, 4304132.308544106, 4536014.662674361, 4883270.07418694, 4969824.694424726]]}
Used in use cases (1 recipe)
Actuary & risk analyst › Claims reserving: chain ladder, Mack uncertainty and Bornhuetter-Ferguson
Actuary & risk analyst › Claims reserving: chain ladder, Mack uncertainty and Bornhuetter-Ferguson
actu bf <json_triangle> <json_premiums> <loss_ratio>
Description
Bornhuetter-Ferguson: the reserve of each origin = premium x expected loss ratio x share not yet reported (from the chain ladder)
Bornhuetter-Ferguson: the reserve of each origin = premium x expected loss ratio x share not yet reported (from the chain ladder)
Parameters
json_triangle: The cumulative triangle - String - required
json_premiums: The premiums of each origin - String - required
loss_ratio: The expected loss ratio - Number - required
json_triangle: The cumulative triangle - String - required
json_premiums: The premiums of each origin - String - required
loss_ratio: The expected loss ratio - Number - required
admin
actu bf "[[1000, 1800, 2100, 2200], [1100, 2000, 2350, null], [1250, 2200, null, null], [1300, null, null, null]]" "[3000, 3200, 3400, 3600]" 0.7
mentdb
{"method": "bf", "expected_loss_ratio": 0.7, "origins": [{"origin": 0, "latest": 2200, "reported_share": 1, "expected_ultimate": 2100, "reserve": 0, "ultimate": 2200}, {"origin": 1, "latest": 2350, "reported_share": 0.9545454545454545, "expected_ultimate": 2240, "reserve": 101.81818181818198, "ultimate": 2451.818181818182}, {"origin": 2, "latest": 2200, "reported_share": 0.81511746680286, "expected_ultimate": 2380, "reserve": 440.02042900919315, "ultimate": 2640.0204290091933}, {"origin": 3, "latest": 1300, "reported_share": 0.4551072522982635, "expected_ultimate": 2520, "reserve": 1373.1297242083758, "ultimate": 2673.1297242083756}], "total_reserve": 1914.968335035751, "chain_ladder_reserve": 2167.3717876781507}
actu bf <json_triangle> <json_premiums> <loss_ratio> <json_params>
Description
Bornhuetter-Ferguson with parameters: method (bf or cape_cod: the loss ratio estimated from the data, the third argument is then ignored), incremental, tail
Bornhuetter-Ferguson with parameters: method (bf or cape_cod: the loss ratio estimated from the data, the third argument is then ignored), incremental, tail
Parameters
json_triangle: The triangle - String - required
json_premiums: The premiums - String - required
loss_ratio: The loss ratio - Number - required
json_params: The parameters - String - required
json_triangle: The triangle - String - required
json_premiums: The premiums - String - required
loss_ratio: The loss ratio - Number - required
json_params: The parameters - String - required
admin
actu bf "[[1000, 1800, 2100, 2200], [1100, 2000, 2350, null], [1250, 2200, null, null], [1300, null, null, null]]" "[3000, 3200, 3400, 3600]" 0 "{\"method\": \"cape_cod\"}"
mentdb
{"method": "cape_cod", "expected_loss_ratio": 0.7692799509594342, "origins": [{"origin": 0, "latest": 2200, "reported_share": 1, "expected_ultimate": 2307.8398528783027, "reserve": 0, "ultimate": 2200}, {"origin": 1, "latest": 2350, "reported_share": 0.9545454545454545, "expected_ultimate": 2461.6958430701898, "reserve": 111.89526559409971, "ultimate": 2461.8952655941}, {"origin": 2, "latest": 2200, "reported_share": 0.81511746680286, "expected_ultimate": 2615.5518332620763, "reserve": 483.56984864191617, "ultimate": 2683.569848641916}, {"origin": 3, "latest": 1300, "reported_share": 0.4551072522982635, "expected_ultimate": 2769.4078234539634, "reserve": 1509.0302384285155, "ultimate": 2809.0302384285155}], "total_reserve": 2104.4953526645313, "chain_ladder_reserve": 2167.3717876781507}
Used in use cases (1 recipe)
Actuary & risk analyst › Claims reserving: chain ladder, Mack uncertainty and Bornhuetter-Ferguson
Actuary & risk analyst › Claims reserving: chain ladder, Mack uncertainty and Bornhuetter-Ferguson
actu life_table <json_qx>
Description
Life table from the qx: lx, dx, Lx, Tx, complete and curtate life expectancies
Life table from the qx: lx, dx, Lx, Tx, complete and curtate life expectancies
Parameters
json_qx: The qx from age 0 - String - required
json_qx: The qx from age 0 - String - required
admin
actu life_table "[0.004, 0.001, 0.0008, 0.0009, 0.0011, 0.5, 1]"
mentdb
{"radix": 100000, "life_expectancy_at_birth": 5.966856054011355, "table": [{"age": 0, "qx": 0.004, "lx": 100000, "dx": 400, "Lx": 99800, "Tx": 596685.6054011355, "ex": 5.966856054011355, "curtate_ex": 5.466856054011355}, {"age": 1, "qx": 0.001, "lx": 99600, "dx": 99.60000000000001, "Lx": 99550.2, "Tx": 496885.6054011355, "ex": 4.988811299208188, "curtate_ex": 4.488811299208188}, {"age": 2, "qx": 8.0E-4, "lx": 99500.4, "dx": 79.60032, "Lx": 99460.59984, "Tx": 397335.4054011355, "ex": 3.993304603812, "curtate_ex": 3.4933046038119997}, {"age": 3, "qx": 9.0E-4, "lx": 99420.79968, "dx": 89.478719712, "Lx": 99376.060320144, "Tx": 297874.8055611355, "ex": 2.996101485, "curtate_ex": 2.4961014849999996}, {"age": 4, "qx": 0.0011, "lx": 99331.320960288, "dx": 109.2644530563168, "Lx": 99276.68873375983, "Tx": 198498.74524099153, "ex": 1.99835, "curtate_ex": 1.49835}, {"age": 5, "qx": 0.5, "lx": 99222.05650723168, "dx": 49611.02825361584, "Lx": 74416.54238042377, "Tx": 99222.05650723168, "ex": 1, "curtate_ex": 0.5}, {"age": 6, "qx": 1, "lx": 49611.02825361584, "dx": 49611.02825361584, "Lx": 24805.51412680792, "Tx": 24805.51412680792, "ex": 0.5, "curtate_ex": 0}]}
actu life_table <json_table> <json_params>
Description
Life table with parameters: input (qx or lx), radix (100000), age0
Life table with parameters: input (qx or lx), radix (100000), age0
Parameters
json_table: The qx or the lx - String - required
json_params: The parameters - String - required
json_table: The qx or the lx - String - required
json_params: The parameters - String - required
admin
actu life_table "[100000, 99500, 98900, 97000, 90000, 60000, 20000]" "{\"input\": \"lx\", \"age0\": 60}"
mentdb
{"radix": 100000, "life_expectancy_at_birth": 5.154, "table": [{"age": 60, "qx": 0.0050000000000000044, "lx": 100000, "dx": 500.00000000000045, "Lx": 99750, "Tx": 515400, "ex": 5.154, "curtate_ex": 4.654}, {"age": 61, "qx": 0.0060301507537688925, "lx": 99500, "dx": 600.0000000000048, "Lx": 99200, "Tx": 415650, "ex": 4.1773869346733665, "curtate_ex": 3.677386934673367}, {"age": 62, "qx": 0.01921132457027297, "lx": 98900, "dx": 1899.9999999999966, "Lx": 97950, "Tx": 316450, "ex": 3.1996966632962587, "curtate_ex": 2.6996966632962587}, {"age": 63, "qx": 0.07216494845360821, "lx": 97000, "dx": 6999.999999999996, "Lx": 93500, "Tx": 218500, "ex": 2.252577319587629, "curtate_ex": 1.7525773195876289}, {"age": 64, "qx": 0.33333333333333337, "lx": 90000, "dx": 30000.000000000004, "Lx": 75000, "Tx": 125000, "ex": 1.3888888888888888, "curtate_ex": 0.8888888888888888}, {"age": 65, "qx": 0.6666666666666667, "lx": 60000, "dx": 40000.00000000001, "Lx": 40000, "Tx": 50000, "ex": 0.8333333333333334, "curtate_ex": 0.3333333333333332}, {"age": 66, "qx": 1, "lx": 19999.999999999993, "dx": 19999.999999999993, "Lx": 9999.999999999996, "Tx": 9999.999999999996, "ex": 0.5, "curtate_ex": 0}]}
Used in use cases (1 recipe)
Actuary & risk analyst › Life insurance: life expectancy, endowment premium, reserves and pension annuity
Actuary & risk analyst › Life insurance: life expectancy, endowment premium, reserves and pension annuity
actu annuity <json_qx> <age> <rate>
Description
Present value of a whole life annuity-due of 1 per year at an age and an interest rate
Present value of a whole life annuity-due of 1 per year at an age and an interest rate
Parameters
json_qx: The mortality table - String - required
age: The age - Number - required
rate: The technical interest rate - Number - required
json_qx: The mortality table - String - required
age: The age - Number - required
rate: The technical interest rate - Number - required
admin
actu annuity "[0.00022, 0.00024, 0.000261, 0.000284, 0.000309, 0.000337, 0.000366, 0.000399, 0.000434, 0.000473, 0.000515, 0.00056, 0.00061, 0.000664, 0.000723, 0.000787, 0.000857, 0.000933, 0.001016, 0.001106, 0.001204, 0.001311, 0.001427, 0.001554, 0.001692, 0.001842, 0.002005, 0.002183, 0.002377, 0.002588, 0.002818, 0.003068, 0.00334, 0.003636, 0.003959, 0.00431, 0.004692, 0.005108, 0.005562, 0.006055, 0.006592, 0.007177, 0.007814, 0.008507, 0.009262, 0.010083, 0.010978, 0.011952, 0.013012, 0.014166, 0.015423, 0.016791, 0.018281, 0.019903, 0.021669, 0.023591, 0.025684, 0.027963, 0.030443, 0.033144, 0.036085, 0.039286, 0.042772, 0.046566, 0.050697, 0.055195, 0.060092, 0.065423, 0.071227, 0.077546, 0.084426, 0.091916, 0.10007, 0.108948, 0.118614, 0.129137, 0.140593, 0.153066, 0.166646, 0.18143, 0.197526, 0.21505, 0.234129, 0.2549, 0.277514, 0.302134, 0.328939, 0.358121, 0.389893, 0.424483, 0.462142, 0.503142, 0.547779, 0.596377, 0.649285, 0.706888, 0.769601, 0.837878, 0.912212, 0.993141, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]" 65 0.02
mentdb
{"annuity_factor": 8.629817152480452, "present_value": 8.629817152480452, "age": 65, "timing": "due", "frequency": 1, "term": 0, "deferred": 0}
actu annuity <json_qx> <age> <rate> <json_params>
Description
Annuity with parameters: term (temporary), deferred (years), timing (due or immediate), frequency (12: monthly, Woolhouse), amount (per year), input, age0
Annuity with parameters: term (temporary), deferred (years), timing (due or immediate), frequency (12: monthly, Woolhouse), amount (per year), input, age0
Parameters
json_qx: The table - String - required
age: The age - Number - required
rate: The rate - Number - required
json_params: The parameters - String - required
json_qx: The table - String - required
age: The age - Number - required
rate: The rate - Number - required
json_params: The parameters - String - required
admin
actu annuity "[0.00022, 0.00024, 0.000261, 0.000284, 0.000309, 0.000337, 0.000366, 0.000399, 0.000434, 0.000473, 0.000515, 0.00056, 0.00061, 0.000664, 0.000723, 0.000787, 0.000857, 0.000933, 0.001016, 0.001106, 0.001204, 0.001311, 0.001427, 0.001554, 0.001692, 0.001842, 0.002005, 0.002183, 0.002377, 0.002588, 0.002818, 0.003068, 0.00334, 0.003636, 0.003959, 0.00431, 0.004692, 0.005108, 0.005562, 0.006055, 0.006592, 0.007177, 0.007814, 0.008507, 0.009262, 0.010083, 0.010978, 0.011952, 0.013012, 0.014166, 0.015423, 0.016791, 0.018281, 0.019903, 0.021669, 0.023591, 0.025684, 0.027963, 0.030443, 0.033144, 0.036085, 0.039286, 0.042772, 0.046566, 0.050697, 0.055195, 0.060092, 0.065423, 0.071227, 0.077546, 0.084426, 0.091916, 0.10007, 0.108948, 0.118614, 0.129137, 0.140593, 0.153066, 0.166646, 0.18143, 0.197526, 0.21505, 0.234129, 0.2549, 0.277514, 0.302134, 0.328939, 0.358121, 0.389893, 0.424483, 0.462142, 0.503142, 0.547779, 0.596377, 0.649285, 0.706888, 0.769601, 0.837878, 0.912212, 0.993141, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]" 55 0.015 "{\"deferred\": 10, \"frequency\": 12, \"amount\": 12000}"
mentdb
{"annuity_factor": 5.04440433992501, "present_value": 60532.85207910012, "age": 55, "timing": "due", "frequency": 12, "term": 0, "deferred": 10}
Used in use cases (1 recipe)
Actuary & risk analyst › Life insurance: life expectancy, endowment premium, reserves and pension annuity
Actuary & risk analyst › Life insurance: life expectancy, endowment premium, reserves and pension annuity
actu insurance <json_qx> <age> <rate>
Description
Whole life insurance of 1 (paid at the end of the year of death): net single premium and level annual net premium
Whole life insurance of 1 (paid at the end of the year of death): net single premium and level annual net premium
Parameters
json_qx: The mortality table - String - required
age: The age - Number - required
rate: The rate - Number - required
json_qx: The mortality table - String - required
age: The age - Number - required
rate: The rate - Number - required
admin
actu insurance "[0.00022, 0.00024, 0.000261, 0.000284, 0.000309, 0.000337, 0.000366, 0.000399, 0.000434, 0.000473, 0.000515, 0.00056, 0.00061, 0.000664, 0.000723, 0.000787, 0.000857, 0.000933, 0.001016, 0.001106, 0.001204, 0.001311, 0.001427, 0.001554, 0.001692, 0.001842, 0.002005, 0.002183, 0.002377, 0.002588, 0.002818, 0.003068, 0.00334, 0.003636, 0.003959, 0.00431, 0.004692, 0.005108, 0.005562, 0.006055, 0.006592, 0.007177, 0.007814, 0.008507, 0.009262, 0.010083, 0.010978, 0.011952, 0.013012, 0.014166, 0.015423, 0.016791, 0.018281, 0.019903, 0.021669, 0.023591, 0.025684, 0.027963, 0.030443, 0.033144, 0.036085, 0.039286, 0.042772, 0.046566, 0.050697, 0.055195, 0.060092, 0.065423, 0.071227, 0.077546, 0.084426, 0.091916, 0.10007, 0.108948, 0.118614, 0.129137, 0.140593, 0.153066, 0.166646, 0.18143, 0.197526, 0.21505, 0.234129, 0.2549, 0.277514, 0.302134, 0.328939, 0.358121, 0.389893, 0.424483, 0.462142, 0.503142, 0.547779, 0.596377, 0.649285, 0.706888, 0.769601, 0.837878, 0.912212, 0.993141, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]" 40 0.02
mentdb
{"type": "whole_life", "net_single_premium": 0.602997342680334, "annual_net_premium": 0.029781859364072984, "premium_annuity": 20.247135523302926}
actu insurance <json_qx> <age> <rate> <json_params>
Description
Insurance with parameters: type (whole_life, term, endowment, pure_endowment), term, benefit, premium_years, reserve_years (prospective net reserves)
Insurance with parameters: type (whole_life, term, endowment, pure_endowment), term, benefit, premium_years, reserve_years (prospective net reserves)
Parameters
json_qx: The table - String - required
age: The age - Number - required
rate: The rate - Number - required
json_params: The parameters - String - required
json_qx: The table - String - required
age: The age - Number - required
rate: The rate - Number - required
json_params: The parameters - String - required
admin
actu insurance "[0.00022, 0.00024, 0.000261, 0.000284, 0.000309, 0.000337, 0.000366, 0.000399, 0.000434, 0.000473, 0.000515, 0.00056, 0.00061, 0.000664, 0.000723, 0.000787, 0.000857, 0.000933, 0.001016, 0.001106, 0.001204, 0.001311, 0.001427, 0.001554, 0.001692, 0.001842, 0.002005, 0.002183, 0.002377, 0.002588, 0.002818, 0.003068, 0.00334, 0.003636, 0.003959, 0.00431, 0.004692, 0.005108, 0.005562, 0.006055, 0.006592, 0.007177, 0.007814, 0.008507, 0.009262, 0.010083, 0.010978, 0.011952, 0.013012, 0.014166, 0.015423, 0.016791, 0.018281, 0.019903, 0.021669, 0.023591, 0.025684, 0.027963, 0.030443, 0.033144, 0.036085, 0.039286, 0.042772, 0.046566, 0.050697, 0.055195, 0.060092, 0.065423, 0.071227, 0.077546, 0.084426, 0.091916, 0.10007, 0.108948, 0.118614, 0.129137, 0.140593, 0.153066, 0.166646, 0.18143, 0.197526, 0.21505, 0.234129, 0.2549, 0.277514, 0.302134, 0.328939, 0.358121, 0.389893, 0.424483, 0.462142, 0.503142, 0.547779, 0.596377, 0.649285, 0.706888, 0.769601, 0.837878, 0.912212, 0.993141, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]" 40 0.02 "{\"type\": \"endowment\", \"term\": 20, \"benefit\": 100000, \"reserve_years\": [5, 10, 15]}"
mentdb
{"type": "endowment", "net_single_premium": 70411.84441210274, "annual_net_premium": 4666.138773455829, "premium_annuity": 15.08995934982757, "reserves": [{"year": 5, "reserve": 21224.038302110028}, {"year": 10, "reserve": 44170.10763077829}, {"year": 15, "reserve": 69706.0495883987}]}
Used in use cases (1 recipe)
Actuary & risk analyst › Life insurance: life expectancy, endowment premium, reserves and pension annuity
Actuary & risk analyst › Life insurance: life expectancy, endowment premium, reserves and pension annuity
actu credibility <json_claims>
Description
Buhlmann credibility of risks observed several years: within and between variances, credibility factor Z and premium of each risk
Buhlmann credibility of risks observed several years: within and between variances, credibility factor Z and premium of each risk
Parameters
json_claims: The claims (one row per risk, one column per year) - String - required
json_claims: The claims (one row per risk, one column per year) - String - required
admin
actu credibility "[[625, 675, 600, 700], [750, 800, 650, 800], [900, 700, 850, 950]]"
mentdb
{"collective_mean": 750, "within_variance": 6250, "between_variance": 8437.5, "risks": [{"risk": "risk0", "own_mean": 650, "weight": 4, "credibility": 0.84375, "premium": 665.625}, {"risk": "risk1", "own_mean": 750, "weight": 4, "credibility": 0.84375, "premium": 750}, {"risk": "risk2", "own_mean": 850, "weight": 4, "credibility": 0.84375, "premium": 834.375}], "k": 0.7407407407407407}
actu credibility <json_claims> <json_params>
Description
Credibility with parameters: weights (Buhlmann-Straub: exposures, the claims are then ratios per unit), names
Credibility with parameters: weights (Buhlmann-Straub: exposures, the claims are then ratios per unit), names
Parameters
json_claims: The claims - String - required
json_params: The parameters - String - required
json_claims: The claims - String - required
json_params: The parameters - String - required
admin
actu credibility "[[0.06, 0.08, 0.05], [0.12, 0.10, 0.14], [0.07, 0.09, 0.08]]" "{\"weights\": [[100, 120, 110], [40, 45, 50], [300, 310, 320]], \"names\": [\"fleet A\", \"fleet B\", \"fleet C\"]}"
mentdb
{"collective_mean": 0.08573480067369724, "within_variance": 0.025465660186090294, "between_variance": 3.775715223513965E-4, "risks": [{"risk": "fleet A", "own_mean": 0.06393939393939395, "weight": 330, "credibility": 0.8303016337713297, "premium": 0.06763803885349456}, {"risk": "fleet B", "own_mean": 0.12074074074074075, "weight": 135, "credibility": 0.6668447423345896, "premium": 0.10907832775788495}, {"risk": "fleet C", "own_mean": 0.08010752688172043, "weight": 930, "credibility": 0.9323813729244408, "premium": 0.08048803540971218}], "k": 67.44592396030872}