Summary of significant accounting policies - Schedule of investments in debt and equity of affiliates (Details) - USD ($) $ in Thousands	Dec. 31, 2018	Dec. 31, 2017
Investments in and Advances to Affiliates [Line Items]
Real Estate Securities, Excess MSRs and Loans, at fair value (1)(2)	$ 214,564	$ 88,349
Investment in debt and equity of affiliates	84,892	99,696
Financing arrangements	(139,739)	(7,184)
Other assets/(liabilities)	(10,293)	620
ARC Home LLC [Member]
Investments in and Advances to Affiliates [Line Items]
Investment in debt and equity of affiliates	20,360	17,911
Residential and Commercial Real Estates Assets [Member]
Investments in and Advances to Affiliates [Line Items]
Real Estate Securities, Excess MSRs and Loans, at fair value (1)(2)	214,600	88,300
Mortgage Acquisition Trust [Member] \| Residential and Commercial Real Estates Assets [Member]
Investments in and Advances to Affiliates [Line Items]
Real Estate Securities, Excess MSRs and Loans, at fair value (1)(2)	$ 113,300	$ 3,900

This item represents the carrying amount of securities and loans held through affiliated entities.

No definition available.

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

- Definition

Investments In And Advances To Affiliates, Other Assets (Liabilities)

+ References

No definition available.

+ Details

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

- Definition

Value of the investment at close of period. For investment in and advances to affiliates, if operations of any controlled companies are different in character from those of the company, group such affiliates within divisions and by type of activities.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 946
-SubTopic 320
-Section S99
-Paragraph 6
-Subparagraph (SX 210.12-14(Column E))
-URI http://asc.fasb.org/extlink&oid=50485924&loc=d3e611322-123010

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 946
-SubTopic 320
-Section S99
-Paragraph 6
-Subparagraph (SX 210.12-14(2))
-URI http://asc.fasb.org/extlink&oid=50485924&loc=d3e611322-123010

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 946
-SubTopic 320
-Section S99
-Paragraph 6
-Subparagraph (SX 210.12-14(3))
-URI http://asc.fasb.org/extlink&oid=50485924&loc=d3e611322-123010

+ Details

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_InvestmentsInAndAdvancesToAffiliatesLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying value, as of the balance sheet date, of securities sold under agreements to repurchase where the transferor maintains effective control over the assets, accounting for them as secured debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-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=26873400&loc=d3e23780-122690

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 860
-SubTopic 10
-Section 55
-Paragraph 51
-URI http://asc.fasb.org/extlink&oid=77903054&loc=d3e101761-111710

+ Details

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

- Details

Name:	us-gaap_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis=mitt_ArcHomeLlcMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ProductOrServiceAxis=mitt_ResidentialAndCommercialRealEstatesAssetsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	dei_LegalEntityAxis=mitt_MortgageAcquisitionTrustMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: