0000001 - Document - Cover link:presentationLink link:calculationLink link:definitionLink 9952151 - Statement - CONDENSED CONSOLIDATED BALANCE SHEETS (unaudited) link:presentationLink link:calculationLink link:definitionLink 9952152 - Statement - CONDENSED CONSOLIDATED BALANCE SHEETS (unaudited) (Parenthetical) link:presentationLink link:calculationLink link:definitionLink 9952153 - Statement - CONDENSED CONSOLIDATED INCOME STATEMENTS (unaudited) link:presentationLink link:calculationLink link:definitionLink 9952154 - Statement - CONDENSED CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (unaudited) link:presentationLink link:calculationLink link:definitionLink 9952155 - Statement - CONDENSED CONSOLIDATED STATEMENTS OF CHANGES IN STOCKHOLDERS' EQUITY AND NONCONTROLLING INTERESTS (unaudited) link:presentationLink link:calculationLink link:definitionLink 9952156 - Statement - CONDENSED CONSOLIDATED STATEMENTS OF CHANGES IN STOCKHOLDERS' EQUITY AND NONCONTROLLING INTERESTS (unaudited) (Parenthetical) link:presentationLink link:calculationLink link:definitionLink 9952157 - Statement - CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS (unaudited) link:presentationLink link:calculationLink link:definitionLink 9952158 - Statement - CONDENSED CONSOLIDATED INCOME STATEMENTS (unaudited) (Parenthetical) link:presentationLink link:calculationLink link:definitionLink 9952159 - Disclosure - Organization link:presentationLink link:calculationLink link:definitionLink 9952160 - Disclosure - Summary of significant accounting policies and estimates link:presentationLink link:calculationLink link:definitionLink 9952161 - Disclosure - Financial Instruments - Credit Losses link:presentationLink link:calculationLink link:definitionLink 9952162 - Disclosure - Leases link:presentationLink link:calculationLink link:definitionLink 9952163 - Disclosure - Revenue from contracts with customers link:presentationLink link:calculationLink link:definitionLink 9952164 - Disclosure - Earnings per share link:presentationLink link:calculationLink link:definitionLink 9952165 - Disclosure - Receivable from and payable to brokers, dealers and clearing organizations link:presentationLink link:calculationLink link:definitionLink 9952166 - Disclosure - Fair value measurements link:presentationLink link:calculationLink link:definitionLink 9952167 - Disclosure - Collateralized transactions link:presentationLink link:calculationLink link:definitionLink 9952168 - Disclosure - Variable interest entities ("VIEs") link:presentationLink link:calculationLink link:definitionLink 9952169 - Disclosure - Income taxes link:presentationLink link:calculationLink link:definitionLink 9952170 - Disclosure - Stockholders' Equity link:presentationLink link:calculationLink link:definitionLink 9952171 - Disclosure - Commitments and Contingencies link:presentationLink link:calculationLink link:definitionLink 9952172 - Disclosure - Regulatory requirements link:presentationLink link:calculationLink link:definitionLink 9952173 - Disclosure - Segment information link:presentationLink link:calculationLink link:definitionLink 9952174 - Disclosure - Subsequent events link:presentationLink link:calculationLink link:definitionLink 9955511 - Disclosure - Summary of significant accounting policies and estimates (Policies) link:presentationLink link:calculationLink link:definitionLink 9955512 - Disclosure - Financial Instruments - Credit Losses (Tables) link:presentationLink link:calculationLink link:definitionLink 9955513 - Disclosure - Leases (Tables) link:presentationLink link:calculationLink link:definitionLink 9955514 - Disclosure - Revenue from contracts with customers (Tables) link:presentationLink link:calculationLink link:definitionLink 9955515 - Disclosure - Earnings per share (Tables) link:presentationLink link:calculationLink link:definitionLink 9955516 - Disclosure - Receivable from and payable to brokers, dealers and clearing organizations (Tables) link:presentationLink link:calculationLink link:definitionLink 9955517 - Disclosure - Fair value measurements (Tables) link:presentationLink link:calculationLink link:definitionLink 9955518 - Disclosure - Collateralized transactions (Tables) link:presentationLink link:calculationLink link:definitionLink 9955519 - Disclosure - Variable interest entities ("VIEs") (Tables) link:presentationLink link:calculationLink link:definitionLink 9955520 - Disclosure - Stockholders' Equity (Tables) link:presentationLink link:calculationLink link:definitionLink 9955521 - Disclosure - Segment information (Tables) link:presentationLink link:calculationLink link:definitionLink 9955522 - Disclosure - Organization (Details) link:presentationLink link:calculationLink link:definitionLink 9955523 - Disclosure - Financial Instruments - Credit Losses - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955524 - Disclosure - Financial Instruments - Credit Losses - Schedule of Disaggregation of Defaulted Notes by Year of Default (Details) link:presentationLink link:calculationLink link:definitionLink 9955525 - Disclosure - Financial Instruments - Credit Losses - Schedule of Activity in Allowance for Uncollectibles of Defaulted Notes (Details) link:presentationLink link:calculationLink link:definitionLink 9955526 - Disclosure - Leases - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955527 - Disclosure - Leases - Schedule of Weighted Average Lease Term and Weighted Average Discount Rate (Details) link:presentationLink link:calculationLink link:definitionLink 9955528 - Disclosure - Leases - Schedule of Operating Lease Costs (Details) link:presentationLink link:calculationLink link:definitionLink 9955529 - Disclosure - Leases - Schedule of Maturities of Lease Liabilities (Details) link:presentationLink link:calculationLink link:definitionLink 9955529 - Disclosure - Leases - Schedule of Maturities of Lease Liabilities (Details) link:presentationLink link:calculationLink link:definitionLink 9955530 - Disclosure - Revenue from contracts with customers - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955531 - Disclosure - Revenue from contracts with customers - Schedule of Disaggregation of Revenue (Details) link:presentationLink link:calculationLink link:definitionLink 9955532 - Disclosure - Revenue from contracts with customers - Schedule of Receivables and Deferred Revenue Balances from Contracts with Customers (Details) link:presentationLink link:calculationLink link:definitionLink 9955533 - Disclosure - Earnings per share - Schedule of Earnings Per Share (Details) link:presentationLink link:calculationLink link:definitionLink 9955534 - Disclosure - Receivable from and payable to brokers, dealers and clearing organizations (Details) link:presentationLink link:calculationLink link:definitionLink 9955535 - Disclosure - Fair value measurements - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955536 - Disclosure - Fair value measurements - Schedule of Investments in Company-Sponsored Funds (Details) link:presentationLink link:calculationLink link:definitionLink 9955537 - Disclosure - Fair value measurements - Schedule of Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) link:presentationLink link:calculationLink link:definitionLink 9955538 - Disclosure - Fair value measurements - Schedule of Changes in Level 3 Assets and Liabilities Measured at Fair Value on a Recurring Basis (Details) link:presentationLink link:calculationLink link:definitionLink 9955539 - Disclosure - Fair value measurements - Schedule of Assets and Liabilities Not Measured at Fair Value (Details) link:presentationLink link:calculationLink link:definitionLink 9955540 - Disclosure - Fair value measurements - Schedule of Notional Amounts and Fair Values of Derivatives by Product (Details) link:presentationLink link:calculationLink link:definitionLink 9955541 - Disclosure - Fair value measurements - Schedule of Fair Value Amounts of Derivative Instruments and their Effect on Consolidated Income Statements (Details) link:presentationLink link:calculationLink link:definitionLink 9955541 - Disclosure - Fair value measurements - Schedule of Fair Value Amounts of Derivative Instruments and their Effect on Consolidated Income Statements (Details) link:presentationLink link:calculationLink link:definitionLink 9955542 - Disclosure - Collateralized transactions - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955543 - Disclosure - Collateralized transactions - Schedule of Disaggregation of Gross Obligation by Class of Collateral Pledged and Remaining Contractual Maturity of Repurchase Agreements and Securities Loaned Transactions (Details) link:presentationLink link:calculationLink link:definitionLink 9955544 - Disclosure - Collateralized transactions - Schedule of Gross Amounts and Offsetting Amounts of Reverse Repurchase Agreements, Repurchase Agreements, Securities Borrowed and Securities Loaned Transactions (Details) link:presentationLink link:calculationLink link:definitionLink 9955545 - Disclosure - Variable interest entities ("VIEs") - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955546 - Disclosure - Variable interest entities ("VIEs") - Assets and Liabilities (Details) link:presentationLink link:calculationLink link:definitionLink 9955547 - Disclosure - Variable interest entities ("VIEs") - Schedule of Unfunded Commitments VIEs (Details) link:presentationLink link:calculationLink link:definitionLink 9955547 - Disclosure - Variable interest entities ("VIEs") - Schedule of Unfunded Commitments VIEs (Details) link:presentationLink link:calculationLink link:definitionLink 9955548 - Disclosure - Income taxes (Details) link:presentationLink link:calculationLink link:definitionLink 9955549 - Disclosure - Stockholders' Equity - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955550 - Disclosure - Stockholders' Equity - Schedule of Changes in Number of Shares of Class A Stock Outstanding (Details) link:presentationLink link:calculationLink link:definitionLink 9955551 - Disclosure - Commitments and Contingencies (Details) link:presentationLink link:calculationLink link:definitionLink 9955552 - Disclosure - Regulatory requirements (Details) link:presentationLink link:calculationLink link:definitionLink 9955553 - Disclosure - Segment information - Narrative (Details) link:presentationLink link:calculationLink link:definitionLink 9955554 - Disclosure - Segment information - Schedule of Reported Revenue and Pre-Tax Income (Loss) (Details) link:presentationLink link:calculationLink link:definitionLink 9955555 - Disclosure - Segment information - Schedule of Revenue Classified by Major Geographic Areas (Details) link:presentationLink link:calculationLink link:definitionLink