Financing arrangements - Summary of financing arrangements (Details) - USD ($)	12 Months Ended
Dec. 31, 2021	Dec. 31, 2020
Repurchase Agreements
Carrying Value	$ 1,777,743,000	$ 500,914,000
Weighted Average Funding Cost	1.75%
Weighted Average Life	3 months 29 days
Collateral, Amortized Cost Basis	$ 2,012,985,000
Collateral, Fair Value	$ 2,033,786,000
Weighted Average Funding Cost	1.75%
Weighted Average Life	3 months 29 days
Collateral, Amortized Cost Basis	$ 2,012,985,000
Collateral, Fair Value	2,033,786,000
Financing arrangements	1,777,743,000	564,047,000
Cash pledged (i.e., restricted cash) under repurchase agreements	5,000,000
Revolving Credit Facility \| Commercial Loans
Repurchase Agreements
Long-term Debt	$ 0	63,133,000
Weighted Average Funding Cost	0.00%
Collateral, Amortized Cost Basis	$ 0
Collateral, Fair Value	0
Residential Mortgage
Repurchase Agreements
Carrying Value	$ 1,286,287,000	0
Weighted Average Funding Cost	2.25%
Weighted Average Life	4 months 24 days
Collateral, Amortized Cost Basis	$ 1,459,876,000
Collateral, Fair Value	$ 1,469,358,000
Debt interest rate	2.18%
Residential Mortgage \| Variable Interest Entity, Primary Beneficiary
Repurchase Agreements
Carrying Value	$ 71,308,000	25,590,000
Weighted Average Funding Cost	1.90%
Weighted Average Life	1 month 20 days
Collateral, Amortized Cost Basis	$ 102,292,000
Collateral, Fair Value	119,947,000
Agency RMBS
Repurchase Agreements
Carrying Value	$ 409,935,000	435,893,000
Weighted Average Funding Cost	0.15%
Weighted Average Life	1 month 17 days
Collateral, Amortized Cost Basis	$ 432,652,000
Collateral, Fair Value	426,486,000
Non-Agency RMBS
Repurchase Agreements
Carrying Value	$ 10,213,000	14,550,000
Weighted Average Funding Cost	1.85%
Weighted Average Life	1 month 13 days
Collateral, Amortized Cost Basis	$ 18,165,000
Collateral, Fair Value	17,995,000
Non-QM Loans \| Counterparty One and Two
Repurchase Agreements
Line of credit facility, maximum borrowing capacity	1,300,000,000
GSE Non-Owner Occupied Loans \| Counterparty One and Two
Repurchase Agreements
Line of credit facility, maximum borrowing capacity	1,000,000,000
CMBS
Repurchase Agreements
Carrying Value	$ 0	$ 24,881,000
Weighted Average Funding Cost	0.00%
Collateral, Amortized Cost Basis	$ 0
Collateral, Fair Value	$ 0

Represents the weighted average funding cost for assets sold under agreements to repurchase.

No definition available.

Name:	mitt_AssetsSoldUnderAgreementsToRepurchaseWeightedAverageFundingCost
Namespace Prefix:	mitt_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Assets Sold Under Agreements To Repurchase Weighted Average Life

+ References

No definition available.

+ Details

Name:	mitt_AssetsSoldUnderAgreementsToRepurchaseWeightedAverageLife
Namespace Prefix:	mitt_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Instrument, Amortized Cost Basis

+ References

No definition available.

+ Details

Name:	mitt_DebtInstrumentAmortizedCostBasis
Namespace Prefix:	mitt_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Debt Instrument, Weighted Average Funding Cost

+ References

No definition available.

+ Details

Name:	mitt_DebtInstrumentWeightedAverageFundingCost
Namespace Prefix:	mitt_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Instrument, Weighted Average Life

+ References

No definition available.

+ Details

Name:	mitt_DebtInstrumentWeightedAverageLife
Namespace Prefix:	mitt_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Pledged Assets Separately Reported, Securities Pledged For Repurchase Agreements, Amortized Cost Basis

+ References

No definition available.

+ Details

Name:	mitt_PledgedAssetsSeparatelyReportedSecuritiesPledgedForRepurchaseAgreementsAmortizedCostBasis
Namespace Prefix:	mitt_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Repurchase Agreements

+ References

No definition available.

+ Details

Name:	mitt_RepurchaseAgreementsAbstract
Namespace Prefix:	mitt_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying amount of assets sold under agreements to repurchase when the carrying amount (or market value, if higher than the carrying amount) of securities or other assets sold under repurchase agreements exceeds 10 percent of total assets.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(m)(1)(i))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e23780-122690

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(m)(1)(ii)(A)(i))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e23780-122690

+ Details

Name:	us-gaap_AssetsSoldUnderAgreementsToRepurchaseCarryingAmounts
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying amount as of the balance sheet date of cash collateral held for borrowed securities, for which the cash is restricted as to withdrawal or usage.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.1)
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03.(a),2)
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

+ Details

Name:	us-gaap_CashCollateralForBorrowedSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of assets pledged to secure a debt instrument.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 50
-Paragraph 3
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=123599511&loc=d3e64711-112823

+ Details

Name:	us-gaap_DebtInstrumentCollateralAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1B
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123466505&loc=SL123495323-112611

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Represents the aggregate of total long-term debt, including current maturities and short-term debt.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtLongtermAndShorttermCombinedAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(3)
-URI http://asc.fasb.org/extlink&oid=123466204&loc=SL6031897-161870

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69C
-URI http://asc.fasb.org/extlink&oid=123466577&loc=SL123495737-112612

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69B
-URI http://asc.fasb.org/extlink&oid=123466577&loc=SL123495735-112612

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1D
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123466505&loc=SL123495340-112611

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LongTermDebt
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The fair value, as of the date of each statement of financial position presented, of securities which are owned but transferred to serve as collateral for the payment of repurchase agreements, and that are reclassified and separately reported in the statement of financial position because the transferee has the right by contract or custom to sell or re-pledge them.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 860
-SubTopic 30
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=66007379&loc=d3e113888-111728

+ Details

Name:	us-gaap_PledgedAssetsSeparatelyReportedSecuritiesPledgedForRepurchaseAgreementsAtFairValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_ResidentialMortgageMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ConsolidatedEntitiesAxis=us-gaap_VariableInterestEntityPrimaryBeneficiaryMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_ResidentialMortgageBackedSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=mitt_NonQualifiedMortgageLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CounterpartyNameAxis=mitt_CounterpartyOneAndTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_CommercialMortgageBackedSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: