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Stock Option Plans - Stock Option Activity and Related Information (Detail) (USD $)
In Millions, except Per Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]      
Shares Under Option, Beginning balance 8.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 9.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 10.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Shares Under Option, Granted 1.9us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod 1.7us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod 1.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod
Shares Under Option, Exercised (1.7)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised (2.3)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised (2.8)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
Shares Under Option, Forfeited or canceled (0.1)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod (0.1)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod (0.2)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
Shares Under Option, Ending balance 8.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 8.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 9.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Shares Under Option, Exercisable at end of period 2.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber 3.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber 5.1us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber
Shares Under Option, Ending vested and expected to vest 8.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber 8.2us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber 8.9us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber
Weighted Average Exercise Price, Beginning balance $ 31.35us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 28.80us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 27.20us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Weighted Average Exercise Price, Granted $ 46.86us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice $ 39.17us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice $ 35.71us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
Weighted Average Exercise Price, Exercised $ 28.80us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice $ 27.11us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice $ 26.14us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
Weighted Average Exercise Price, Forfeited or canceled $ 28.36us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice $ 26.01us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice $ 29.46us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
Weighted Average Exercised Price, Ending balance $ 35.49us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 31.35us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 28.80us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Weighted Average Exercise Price, Exercisable at end of period $ 26.91us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice $ 27.64us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice $ 27.50us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
Weighted Average Exercise price, Ending vested and expected to vest $ 35.38us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice $ 31.28us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice $ 28.76us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice
Weighted Average Remaining Contractual Term (in years), Ending balance 3 years 11 months 16 days 3 years 7 months 13 days 3 years 4 months 28 days
Weighted Average Remaining Contractual Term (in years), Exercisable at end of period 1 year 10 months 13 days 2 years 1 month 24 days 2 years 6 months 7 days
Weighted Average Remaining Contractual Term (in years), Ending vested and expected to vested 3 years 11 months 5 days 3 years 7 months 2 days 3 years 4 months 21 days
Aggregate Intrinsic Value, Ending Balance $ 97.2ajg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAggregateIntrinsicValue $ 129.4ajg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAggregateIntrinsicValue $ 53.9ajg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAggregateIntrinsicValue
Aggregate Intrinsic Value, Exercisable at end of period 52.8us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1 72.5us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1 36.3us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1
Aggregate Intrinsic Value, Ending vested and expected to vest $ 96.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue $ 128.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue $ 53.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue