<PAGE>   1
                                                                              24




                                                                    Exhibit 11.1




                                MID OCEAN LIMITED

                 STATEMENT OF COMPUTATION OF EARNINGS PER SHARE
                   YEARS ENDED OCTOBER 31, 1997, 1996 AND 1995

                (EXPRESSED IN THOUSANDS OF UNITED STATES DOLLARS
               EXCEPT FOR NUMBER OF SHARES AND EARNINGS PER SHARE)




<TABLE>
<CAPTION>
                                 -------------------------------------------------------------------------------------------
                                             1997                            1996                            1995
                                     Primary           Fully         Primary           Fully         Primary           Fully
                                                     Diluted                         Diluted                         Diluted
                                 -------------------------------------------------------------------------------------------
<S>                              <C>             <C>             <C>             <C>             <C>             <C>
Net Income                       $   245,008     $   245,008     $   211,644     $   211,644     $   182,935     $   182,935

Number of Shares
Weighted average
shares outstanding                37,596,430      37,596,430      34,453,134      34,453,134      35,657,570      35,657,570

Incremental shares of
outstanding options (1)              330,533         353,782         434,588         451,297         271,243         318,597

Incremental shares
of outstanding stock options
of Mid Ocean Reinsurance (2)              --              --       1,951,235       1,997,912       1,417,690       1,555,992
                                 -----------     -----------     -----------     -----------     -----------     -----------


                                  37,926,963      37,950,212      36,838,957      36,902,343      37,346,503      37,532,159
                                 -----------     -----------     -----------     -----------     -----------     -----------

Earnings per share:              $      6.46     $      6.46     $      5.75     $      5.74     $      4.90     $      4.87
                                 -----------     -----------     -----------     -----------     -----------     -----------
</TABLE>




(1) As of October 31, 1997, the Company has 745,368 (1996: 903,454; 1995:
947,838) options outstanding. The dilution on a primary basis would be the
equivalent of approximately 330,533 (1996: 434,588; 1995: 271,243) shares, using
the treasury stock method, based on the average market price.

(2) As of October 31, 1997, Mid Ocean Reinsurance has nil (1996: 560,645; 1995:
560,645) options outstanding. Each holder of Mid Ocean Reinsurance options
entered into a put/call agreement which entitled it to put the shares of Mid
Ocean Reinsurance issued upon the exercise of its options to the Company in
exchange for, at the election of the Company, shares of the Company having a
fair market value or an amount of cash equal to the fair market value of the Mid
Ocean Reinsurance shares so put. These options were exercised during the year
ended October 31, 1997. Such agreements permitted the Company to call any Mid
Ocean Reinsurance shares so issued in exchange for shares of the Company having
a fair market value equal to the fair market value of the Mid Ocean Reinsurance
shares so called. Dilution on a primary basis would be the equivalent of nil
(1996: 1,951,235; 1995: 1,417,690) shares using the treasury stock method, based
on the receipt of six shares of the Company for each share of Mid Ocean
Reinsurance common stock issued upon the exercise of the options and the average
market price for the year.