<Page>

                                                                      EXHIBIT 21

                           SUBSIDIARIES OF REGISTRANT

<Table>
<Caption>
       Name                                               State of Incorporation
       ----                                               ----------------------
                                                       
Arch Reinsurance Ltd.                                           Bermuda

Rock River Insurance Company                                    Wisconsin

Arch Capital Group (U.S.) Inc.                                  Delaware

Hales & Company Inc.                                            Delaware

Arch Reinsurance Company                                        Nebraska

Cross River Insurance Company                                   Nebraska

American Independent Insurance Holding Company                  Pennsylvania

American Independent Insurance Company                          Pennsylvania

Arch Risk Transfer Services Ltd.                                Cayman Islands

Alternative Re Holdings Ltd.                                    Bermuda

Alternative Re, Ltd.                                            Bermuda

First American Financial Corporation                            Missouri

Alternative Insurance Company Limited                           Bermuda

First American Insurance Agency, Inc.                           Missouri

First American Insurance Company                                Missouri
</Table>