FA-63751 / Actuarial life tables / Open access
Net premium reserve recursion: Rounded reserves feed the next year · case 01
Later reserves drift from the exact recursion.
ROOT CAUSE
The reported rounded reserve overwrites the exact carried value.
VERIFIED REPAIR
Carry the exact reserve and round only for reporting.
Unsuccessful approach: Truncating the carried reserve adds a larger drift.
Case contract
Input q (per 100000 by policy year), P (annual net premium, cents, paid at start of year), S (death benefit at year end), i (per mille). Starting from 0V=0: (k+1)V = ((kV+P)(1+i) - q S)/p carried exactly; each reserve is reported rounded half away from zero. If p=0 report None and stop.
Why this case matters
Life-table arithmetic compounds across ages, so one misplaced index or assumption shifts every downstream value.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
V=Fraction(0); i=Fraction(x['i'],1000); out=[]
for q in x['q']:
q=Fraction(q,100000); p=1-q
if p==0: out.append(None); break
V=((V+x['P'])*(1+i)-q*x['S'])/p
V=Fraction(math.floor(V+Fraction(1,2)) if V>=0 else -math.floor(-V+Fraction(1,2))); out.append(int(V))
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['level premium reserve build-up', {'q': [975, 1110, 1287, 1446, 1655, 1872], 'P': 76793, 'S': 10000000, 'i': 50}, [-17033, -48794, -100596, -172081, -270021, -397532]], ['negative early reserves', {'q': [2102, 1644, 1735, 2752, 3106, 3484], 'P': 4838, 'S': 10000000, 'i': 30}, [-209623, -381602, -571482, -883148, -1254215, -1694287]], ['terminal age', {'q': [5297, 5940, 6674, 7478, 100000], 'P': 60841, 'S': 10000000, 'i': 50}, [-491871, -1112675, -1898534, -2893774, None]], ['terminal after one year', {'q': [7910, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-689543, None]], ['high interest', {'q': [1315, 1480, 1689, 1919, 2194], 'P': 32431, 'S': 10000000, 'i': 90}, [-97431, -222138, -382135, -584290, -839341]], ['odd premium', {'q': [2038, 2332, 2622, 2985, 3374], 'P': 58059, 'S': 10000001, 'i': 40}, [-146402, -332839, -562726, -848687, -1200146]], ['zero mortality year', {'q': [0, 366, 1710], 'P': 12345, 'S': 10000000, 'i': 30}, [12715, -10827, -172385]]], [['level premium reserve build-up', {'q': [744, 879, 1007, 1130, 1268, 1430], 'P': 89607, 'S': 10000000, 'i': 30}, [18029, 23169, 15617, -4672, -39822, -93052]], ['negative early reserves', {'q': [2093, 1729, 2954, 2713, 3083, 3497], 'P': 5237, 'S': 10000000, 'i': 40}, [-208211, -390749, -717529, -1040307, -1428823, -1896552]], ['terminal age', {'q': [2713, 3066, 3446, 3884, 100000], 'P': 86120, 'S': 10000000, 'i': 40}, [-186803, -424320, -721180, -1091246, None]], ['terminal after one year', {'q': [6406, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-517768, None]], ['high interest', {'q': [1493, 1714, 1927, 2166, 2437], 'P': 43892, 'S': 10000000, 'i': 90}, [-102995, -239935, -414372, -634159, -909250]], ['odd premium', {'q': [1846, 2072, 2329, 2619, 2943], 'P': 59305, 'S': 10000001, 'i': 40}, [-125235, -281602, -475155, -713059, -1003744]], ['zero mortality year', {'q': [0, 393, 2596], 'P': 12345, 'S': 10000000, 'i': 30}, [12715, -13541, -267784]]], [['level premium reserve build-up', {'q': [1080, 1230, 1415, 1587, 1826, 2063], 'P': 69053, 'S': 10000000, 'i': 30}, [-37278, -91396, -166874, -263640, -390149, -548341]], ['negative early reserves', {'q': [2234, 1739, 1991, 1180, 1338, 1529], 'P': 3869, 'S': 10000000, 'i': 30}, [-224429, -408175, -628039, -769981, -935411, -1129661]], ['terminal age', {'q': [4877, 5479, 6148, 6925, 100000], 'P': 57524, 'S': 10000000, 'i': 40}, [-449812, -1011288, -1711967, -2592662, None]], ['terminal after one year', {'q': [6383, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 50}, [-513582, None]], ['high interest', {'q': [950, 1068, 1246, 1434, 1654], 'P': 43973, 'S': 10000000, 'i': 90}, [-47521, -111862, -201105, -319252, -473282]], ['odd premium', {'q': [1463, 1641, 1842, 2102, 2386], 'P': 35283, 'S': 10000001, 'i': 30}, [-111591, -246746, -409551, -608487, -849263]], ['zero mortality year', {'q': [0, 709, 1372], 'P': 12345, 'S': 10000000, 'i': 50}, [12962, -44644, -173494]]], [['level premium reserve build-up', {'q': [828, 943, 1093, 1268, 1442, 1649], 'P': 48203, 'S': 10000000, 'i': 40}, [-32942, -79175, -143074, -228362, -336416, -472432]], ['negative early reserves', {'q': [2171, 2815, 1676, 2525, 2850, 3242], 'P': 4814, 'S': 10000000, 'i': 50}, [-216751, -518633, -719163, -1028538, -1399804, -1848880]], ['terminal age', {'q': [5153, 5772, 6486, 7287, 100000], 'P': 55714, 'S': 10000000, 'i': 50}, [-481618, -1087150, -1851709, -2819987, None]], ['terminal after one year', {'q': [8017, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-701978, None]], ['high interest', {'q': [2062, 2333, 2619, 2954, 3351], 'P': 54331, 'S': 10000000, 'i': 90}, [-150074, -345725, -595106, -911778, -1313741]], ['odd premium', {'q': [829, 978, 1104, 1247, 1430], 'P': 32765, 'S': 10000001, 'i': 50}, [-48902, -115877, -199875, -303955, -433955]], ['zero mortality year', {'q': [0, 457, 2109], 'P': 12345, 'S': 10000000, 'i': 40}, [12839, -19598, -223150]]], [['level premium reserve build-up', {'q': [1056, 1225, 1381, 1569, 1791, 2046], 'P': 41129, 'S': 10000000, 'i': 30}, [-63912, -147777, -251419, -379453, -537195, -730493]], ['negative early reserves', {'q': [2984, 2967, 1872, 1261, 1429, 1601], 'P': 5163, 'S': 10000000, 'i': 50}, [-301990, -626971, -856125, -1032631, -1239454, -1479797]], ['terminal age', {'q': [2899, 3279, 3718, 4187, 100000], 'P': 83535, 'S': 10000000, 'i': 50}, [-208225, -474379, -812391, -1235739, None]], ['terminal after one year', {'q': [5620, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 50}, [-428587, None]], ['high interest', {'q': [1989, 2255, 2548, 2862, 3235], 'P': 34236, 'S': 10000000, 'i': 90}, [-164862, -376369, -644138, -979012, -1398549]], ['odd premium', {'q': [1087, 1231, 1389, 1601, 1828], 'P': 31067, 'S': 10000001, 'i': 30}, [-77544, -173102, -289213, -432922, -607821]], ['zero mortality year', {'q': [0, 757, 1366], 'P': 12345, 'S': 10000000, 'i': 40}, [12839, -49886, -178076]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| level premium reserve build-up | [-17033, -48794, -100596, -172081, -270021, -397531] | [-17033, -48794, -100596, -172081, -270021, -397532] | Failed |
| negative early reserves | [-209623, -381602, -571482, -883148, -1254215, -1694287] | [-209623, -381602, -571482, -883148, -1254215, -1694287] | Passed |
| terminal age | [-491871, -1112674, -1898533, -2893773, None] | [-491871, -1112675, -1898534, -2893774, None] | Failed |
| terminal after one year | [-689543, None] | [-689543, None] | Passed |
| high interest | [-97431, -222138, -382135, -584290, -839341] | [-97431, -222138, -382135, -584290, -839341] | Passed |
| odd premium | [-146402, -332839, -562726, -848687, -1200146] | [-146402, -332839, -562726, -848687, -1200146] | Passed |
| zero mortality year | [12715, -10828, -172385] | [12715, -10827, -172385] | Failed |
SHA-256 / 7fc7acc140ed848aa601b6cde9a2e90b58e072b261f93100ccd285085cbea35c
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
V=Fraction(0); i=Fraction(x['i'],1000); out=[]
for q in x['q']:
q=Fraction(q,100000); p=1-q
if p==0: out.append(None); break
V=((V+x['P'])*(1+i)-q*x['S'])/p
V=Fraction(int(V)); out.append(int(V))
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['level premium reserve build-up', {'q': [975, 1110, 1287, 1446, 1655, 1872], 'P': 76793, 'S': 10000000, 'i': 50}, [-17033, -48794, -100596, -172081, -270021, -397532]], ['negative early reserves', {'q': [2102, 1644, 1735, 2752, 3106, 3484], 'P': 4838, 'S': 10000000, 'i': 30}, [-209623, -381602, -571482, -883148, -1254215, -1694287]], ['terminal age', {'q': [5297, 5940, 6674, 7478, 100000], 'P': 60841, 'S': 10000000, 'i': 50}, [-491871, -1112675, -1898534, -2893774, None]], ['terminal after one year', {'q': [7910, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-689543, None]], ['high interest', {'q': [1315, 1480, 1689, 1919, 2194], 'P': 32431, 'S': 10000000, 'i': 90}, [-97431, -222138, -382135, -584290, -839341]], ['odd premium', {'q': [2038, 2332, 2622, 2985, 3374], 'P': 58059, 'S': 10000001, 'i': 40}, [-146402, -332839, -562726, -848687, -1200146]], ['zero mortality year', {'q': [0, 366, 1710], 'P': 12345, 'S': 10000000, 'i': 30}, [12715, -10827, -172385]]], [['level premium reserve build-up', {'q': [744, 879, 1007, 1130, 1268, 1430], 'P': 89607, 'S': 10000000, 'i': 30}, [18029, 23169, 15617, -4672, -39822, -93052]], ['negative early reserves', {'q': [2093, 1729, 2954, 2713, 3083, 3497], 'P': 5237, 'S': 10000000, 'i': 40}, [-208211, -390749, -717529, -1040307, -1428823, -1896552]], ['terminal age', {'q': [2713, 3066, 3446, 3884, 100000], 'P': 86120, 'S': 10000000, 'i': 40}, [-186803, -424320, -721180, -1091246, None]], ['terminal after one year', {'q': [6406, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-517768, None]], ['high interest', {'q': [1493, 1714, 1927, 2166, 2437], 'P': 43892, 'S': 10000000, 'i': 90}, [-102995, -239935, -414372, -634159, -909250]], ['odd premium', {'q': [1846, 2072, 2329, 2619, 2943], 'P': 59305, 'S': 10000001, 'i': 40}, [-125235, -281602, -475155, -713059, -1003744]], ['zero mortality year', {'q': [0, 393, 2596], 'P': 12345, 'S': 10000000, 'i': 30}, [12715, -13541, -267784]]], [['level premium reserve build-up', {'q': [1080, 1230, 1415, 1587, 1826, 2063], 'P': 69053, 'S': 10000000, 'i': 30}, [-37278, -91396, -166874, -263640, -390149, -548341]], ['negative early reserves', {'q': [2234, 1739, 1991, 1180, 1338, 1529], 'P': 3869, 'S': 10000000, 'i': 30}, [-224429, -408175, -628039, -769981, -935411, -1129661]], ['terminal age', {'q': [4877, 5479, 6148, 6925, 100000], 'P': 57524, 'S': 10000000, 'i': 40}, [-449812, -1011288, -1711967, -2592662, None]], ['terminal after one year', {'q': [6383, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 50}, [-513582, None]], ['high interest', {'q': [950, 1068, 1246, 1434, 1654], 'P': 43973, 'S': 10000000, 'i': 90}, [-47521, -111862, -201105, -319252, -473282]], ['odd premium', {'q': [1463, 1641, 1842, 2102, 2386], 'P': 35283, 'S': 10000001, 'i': 30}, [-111591, -246746, -409551, -608487, -849263]], ['zero mortality year', {'q': [0, 709, 1372], 'P': 12345, 'S': 10000000, 'i': 50}, [12962, -44644, -173494]]], [['level premium reserve build-up', {'q': [828, 943, 1093, 1268, 1442, 1649], 'P': 48203, 'S': 10000000, 'i': 40}, [-32942, -79175, -143074, -228362, -336416, -472432]], ['negative early reserves', {'q': [2171, 2815, 1676, 2525, 2850, 3242], 'P': 4814, 'S': 10000000, 'i': 50}, [-216751, -518633, -719163, -1028538, -1399804, -1848880]], ['terminal age', {'q': [5153, 5772, 6486, 7287, 100000], 'P': 55714, 'S': 10000000, 'i': 50}, [-481618, -1087150, -1851709, -2819987, None]], ['terminal after one year', {'q': [8017, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-701978, None]], ['high interest', {'q': [2062, 2333, 2619, 2954, 3351], 'P': 54331, 'S': 10000000, 'i': 90}, [-150074, -345725, -595106, -911778, -1313741]], ['odd premium', {'q': [829, 978, 1104, 1247, 1430], 'P': 32765, 'S': 10000001, 'i': 50}, [-48902, -115877, -199875, -303955, -433955]], ['zero mortality year', {'q': [0, 457, 2109], 'P': 12345, 'S': 10000000, 'i': 40}, [12839, -19598, -223150]]], [['level premium reserve build-up', {'q': [1056, 1225, 1381, 1569, 1791, 2046], 'P': 41129, 'S': 10000000, 'i': 30}, [-63912, -147777, -251419, -379453, -537195, -730493]], ['negative early reserves', {'q': [2984, 2967, 1872, 1261, 1429, 1601], 'P': 5163, 'S': 10000000, 'i': 50}, [-301990, -626971, -856125, -1032631, -1239454, -1479797]], ['terminal age', {'q': [2899, 3279, 3718, 4187, 100000], 'P': 83535, 'S': 10000000, 'i': 50}, [-208225, -474379, -812391, -1235739, None]], ['terminal after one year', {'q': [5620, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 50}, [-428587, None]], ['high interest', {'q': [1989, 2255, 2548, 2862, 3235], 'P': 34236, 'S': 10000000, 'i': 90}, [-164862, -376369, -644138, -979012, -1398549]], ['odd premium', {'q': [1087, 1231, 1389, 1601, 1828], 'P': 31067, 'S': 10000001, 'i': 30}, [-77544, -173102, -289213, -432922, -607821]], ['zero mortality year', {'q': [0, 757, 1366], 'P': 12345, 'S': 10000000, 'i': 40}, [12839, -49886, -178076]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| level premium reserve build-up | [-17033, -48793, -100594, -172079, -270019, -397529] | [-17033, -48794, -100596, -172081, -270021, -397532] | Failed |
| negative early reserves | [-209623, -381602, -571482, -883147, -1254214, -1694286] | [-209623, -381602, -571482, -883148, -1254215, -1694287] | Failed |
| terminal age | [-491871, -1112674, -1898532, -2893771, None] | [-491871, -1112675, -1898534, -2893774, None] | Failed |
| terminal after one year | [-689542, None] | [-689543, None] | Failed |
| high interest | [-97431, -222137, -382133, -584287, -839338] | [-97431, -222138, -382135, -584290, -839341] | Failed |
| odd premium | [-146402, -332838, -562724, -848684, -1200142] | [-146402, -332839, -562726, -848687, -1200146] | Failed |
| zero mortality year | [12715, -10827, -172384] | [12715, -10827, -172385] | Failed |
SHA-256 / f3bfde96a57e5e6c8264054ddf1e39dee7a479eecb6b796aca7edf0ba76b500b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
V=Fraction(0); i=Fraction(x['i'],1000); out=[]
for q in x['q']:
q=Fraction(q,100000); p=1-q
if p==0: out.append(None); break
V=((V+x['P'])*(1+i)-q*x['S'])/p
out.append(math.floor(V+Fraction(1,2)) if V>=0 else -math.floor(-V+Fraction(1,2)))
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['level premium reserve build-up', {'q': [975, 1110, 1287, 1446, 1655, 1872], 'P': 76793, 'S': 10000000, 'i': 50}, [-17033, -48794, -100596, -172081, -270021, -397532]], ['negative early reserves', {'q': [2102, 1644, 1735, 2752, 3106, 3484], 'P': 4838, 'S': 10000000, 'i': 30}, [-209623, -381602, -571482, -883148, -1254215, -1694287]], ['terminal age', {'q': [5297, 5940, 6674, 7478, 100000], 'P': 60841, 'S': 10000000, 'i': 50}, [-491871, -1112675, -1898534, -2893774, None]], ['terminal after one year', {'q': [7910, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-689543, None]], ['high interest', {'q': [1315, 1480, 1689, 1919, 2194], 'P': 32431, 'S': 10000000, 'i': 90}, [-97431, -222138, -382135, -584290, -839341]], ['odd premium', {'q': [2038, 2332, 2622, 2985, 3374], 'P': 58059, 'S': 10000001, 'i': 40}, [-146402, -332839, -562726, -848687, -1200146]], ['zero mortality year', {'q': [0, 366, 1710], 'P': 12345, 'S': 10000000, 'i': 30}, [12715, -10827, -172385]]], [['level premium reserve build-up', {'q': [744, 879, 1007, 1130, 1268, 1430], 'P': 89607, 'S': 10000000, 'i': 30}, [18029, 23169, 15617, -4672, -39822, -93052]], ['negative early reserves', {'q': [2093, 1729, 2954, 2713, 3083, 3497], 'P': 5237, 'S': 10000000, 'i': 40}, [-208211, -390749, -717529, -1040307, -1428823, -1896552]], ['terminal age', {'q': [2713, 3066, 3446, 3884, 100000], 'P': 86120, 'S': 10000000, 'i': 40}, [-186803, -424320, -721180, -1091246, None]], ['terminal after one year', {'q': [6406, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-517768, None]], ['high interest', {'q': [1493, 1714, 1927, 2166, 2437], 'P': 43892, 'S': 10000000, 'i': 90}, [-102995, -239935, -414372, -634159, -909250]], ['odd premium', {'q': [1846, 2072, 2329, 2619, 2943], 'P': 59305, 'S': 10000001, 'i': 40}, [-125235, -281602, -475155, -713059, -1003744]], ['zero mortality year', {'q': [0, 393, 2596], 'P': 12345, 'S': 10000000, 'i': 30}, [12715, -13541, -267784]]], [['level premium reserve build-up', {'q': [1080, 1230, 1415, 1587, 1826, 2063], 'P': 69053, 'S': 10000000, 'i': 30}, [-37278, -91396, -166874, -263640, -390149, -548341]], ['negative early reserves', {'q': [2234, 1739, 1991, 1180, 1338, 1529], 'P': 3869, 'S': 10000000, 'i': 30}, [-224429, -408175, -628039, -769981, -935411, -1129661]], ['terminal age', {'q': [4877, 5479, 6148, 6925, 100000], 'P': 57524, 'S': 10000000, 'i': 40}, [-449812, -1011288, -1711967, -2592662, None]], ['terminal after one year', {'q': [6383, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 50}, [-513582, None]], ['high interest', {'q': [950, 1068, 1246, 1434, 1654], 'P': 43973, 'S': 10000000, 'i': 90}, [-47521, -111862, -201105, -319252, -473282]], ['odd premium', {'q': [1463, 1641, 1842, 2102, 2386], 'P': 35283, 'S': 10000001, 'i': 30}, [-111591, -246746, -409551, -608487, -849263]], ['zero mortality year', {'q': [0, 709, 1372], 'P': 12345, 'S': 10000000, 'i': 50}, [12962, -44644, -173494]]], [['level premium reserve build-up', {'q': [828, 943, 1093, 1268, 1442, 1649], 'P': 48203, 'S': 10000000, 'i': 40}, [-32942, -79175, -143074, -228362, -336416, -472432]], ['negative early reserves', {'q': [2171, 2815, 1676, 2525, 2850, 3242], 'P': 4814, 'S': 10000000, 'i': 50}, [-216751, -518633, -719163, -1028538, -1399804, -1848880]], ['terminal age', {'q': [5153, 5772, 6486, 7287, 100000], 'P': 55714, 'S': 10000000, 'i': 50}, [-481618, -1087150, -1851709, -2819987, None]], ['terminal after one year', {'q': [8017, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 40}, [-701978, None]], ['high interest', {'q': [2062, 2333, 2619, 2954, 3351], 'P': 54331, 'S': 10000000, 'i': 90}, [-150074, -345725, -595106, -911778, -1313741]], ['odd premium', {'q': [829, 978, 1104, 1247, 1430], 'P': 32765, 'S': 10000001, 'i': 50}, [-48902, -115877, -199875, -303955, -433955]], ['zero mortality year', {'q': [0, 457, 2109], 'P': 12345, 'S': 10000000, 'i': 40}, [12839, -19598, -223150]]], [['level premium reserve build-up', {'q': [1056, 1225, 1381, 1569, 1791, 2046], 'P': 41129, 'S': 10000000, 'i': 30}, [-63912, -147777, -251419, -379453, -537195, -730493]], ['negative early reserves', {'q': [2984, 2967, 1872, 1261, 1429, 1601], 'P': 5163, 'S': 10000000, 'i': 50}, [-301990, -626971, -856125, -1032631, -1239454, -1479797]], ['terminal age', {'q': [2899, 3279, 3718, 4187, 100000], 'P': 83535, 'S': 10000000, 'i': 50}, [-208225, -474379, -812391, -1235739, None]], ['terminal after one year', {'q': [5620, 100000, 50000], 'P': 150000, 'S': 10000000, 'i': 50}, [-428587, None]], ['high interest', {'q': [1989, 2255, 2548, 2862, 3235], 'P': 34236, 'S': 10000000, 'i': 90}, [-164862, -376369, -644138, -979012, -1398549]], ['odd premium', {'q': [1087, 1231, 1389, 1601, 1828], 'P': 31067, 'S': 10000001, 'i': 30}, [-77544, -173102, -289213, -432922, -607821]], ['zero mortality year', {'q': [0, 757, 1366], 'P': 12345, 'S': 10000000, 'i': 40}, [12839, -49886, -178076]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| level premium reserve build-up | [-17033, -48794, -100596, -172081, -270021, -397532] | [-17033, -48794, -100596, -172081, -270021, -397532] | Passed |
| negative early reserves | [-209623, -381602, -571482, -883148, -1254215, -1694287] | [-209623, -381602, -571482, -883148, -1254215, -1694287] | Passed |
| terminal age | [-491871, -1112675, -1898534, -2893774, None] | [-491871, -1112675, -1898534, -2893774, None] | Passed |
| terminal after one year | [-689543, None] | [-689543, None] | Passed |
| high interest | [-97431, -222138, -382135, -584290, -839341] | [-97431, -222138, -382135, -584290, -839341] | Passed |
| odd premium | [-146402, -332839, -562726, -848687, -1200146] | [-146402, -332839, -562726, -848687, -1200146] | Passed |
| zero mortality year | [12715, -10827, -172385] | [12715, -10827, -172385] | Passed |
SHA-256 / 18e0414258b2a3af63a8679fd545638eebd65578071e3d54630b305f2976a273
Verification & scope
A deterministic bounded teaching model of a stipulated toy actuarial contract. Rates are small synthetic tables, exact rationals are used where practical and floats are rounded at the output; it makes no claim of conformance with any published table, standard of practice or regulation. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:47:17.501233+00:00.
Case digest / 26197af29be2d2efa952f173d1058d43420a9b1d8b996092ef57273a2802b0e3