| **Fair Value Measurements - Level 3 unobservable inputs (Details) - Recurring basis - Level 3 - Internal model pricing** | 9 Months Ended | 12 Months Ended |
|--------------------------------------------------------------------------------------------------------------------------|----------------|-----------------|
||
| Minimum                                                                                                                  |           |            |
| **Unobservable Input**                                                                                                   |           |            |
| Equity volatility                                                                                                        | 15.00%         | 15.00%          |
| Swap curve                                                                                                               | 2.40%          | 1.69%           |
| Base Lapse rate                                                                                                          | 1.00%          | 1.00%           |
| Maximum                                                                                                                  |           |            |
| **Unobservable Input**                                                                                                   |           |            |
| Equity volatility                                                                                                        | 30.00%         | 30.00%          |
| Swap curve                                                                                                               | 3.16%          | 2.54%           |
| Base Lapse rate                                                                                                          | 15.00%         | 15.00%          |

| X                                                                                                                                                                                                                |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Equity Volatility
+ References
No definition available.
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| X                                                                                                                                                                                                  |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Lapse Rate
+ References
No definition available.
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| X                                                                                                                                                                                                  |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - Definition
Swap Curve
+ References
No definition available.
+ Details**Name:**gac_SwapCurve**Namespace Prefix:**gac_**Data Type:**num:percentItemType**Balance Type:**na**Period Type:**duration |
| X                                                                                                                                                                                                 |
|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| - References
No definition available.
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| X                                                                                                                                                                                |
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| X                                                                                                                                                                          |
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| X                                                                                                                                                                               |
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| X                                                                                                                               |
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| X                                                                                                                               |
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