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Share Transactions	3 Months Ended
Share Transactions	Mar. 31, 2021
Stockholders' Equity Note [Abstract]
Share Transactions	Share Transactions Share-Based Compensation During the 2021 first quarter, the Company granted 1,218,465 stock options, 685,104 performance share awards (“PSAs”) and units (“PSUs”) and 1,168,577 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2021 first quarter were approximately $9.20, $37.38 and $35.82 per share, respectively. Such values are being amortized over the respective substantive vesting period. During the 2020 first quarter, the Company granted 1,116,073 stock options, 557,204 PSAs and PSUs and 910,879 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2020 first quarter were approximately $8.14, $44.17 and $42.36 per share, respectively. Such values are being amortized over the respective substantive vesting period. Share Repurchases The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 394.5 million common shares for an aggregate purchase price of $4.23 billion. For the three months ended March 31, 2021, Arch Capital repurchased 5.3 million shares under the share repurchase program with an aggregate purchase price of $179.3 million. Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million during the three months ended March 31, 2020. At March 31, 2021, $737.3 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.