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Reinsurance
 6 Months Ended
Jun. 30, 2024
Reinsurance Disclosures [Abstract]  
Reinsurance Reinsurance
The following tables summarize the effect of reinsurance and retrocessional reinsurance on premiums written and earned.

Quarter Ended June 30,
20242023
(dollars in thousands)DirectAssumedCededNet PremiumsDirectAssumedCededNet Premiums
Underwriting:
Written$2,356,536 $564,851 $(642,448)$2,278,939 $2,285,739 $448,837 $(526,562)$2,208,014 
Earned$2,149,773 $414,488 $(487,002)$2,077,259 $2,025,324 $424,404 $(418,264)$2,031,464 
Program services and other fronting:
Written943,140 847,603 (1,790,903)(160)824,171 229,438 (1,053,930)(321)
Earned811,377 240,844 (1,052,381)(160)649,562 159,075 (808,958)(321)
Consolidated:
Written$3,299,676 $1,412,454 $(2,433,351)$2,278,779 $3,109,910 $678,275 $(1,580,492)$2,207,693 
Earned$2,961,150 $655,332 $(1,539,383)$2,077,099 $2,674,886 $583,479 $(1,227,222)$2,031,143 

Six Months Ended June 30,
20242023
(dollars in thousands)DirectAssumedCededNet PremiumsDirectAssumedCededNet Premiums
Underwriting:
Written$4,464,003 $1,233,550 $(1,186,404)$4,511,149 $4,255,102 $1,137,732 $(966,591)$4,426,243 
Earned$4,348,011 $807,430 $(950,382)$4,205,059 $3,997,200 $823,123 $(820,704)$3,999,619 
Program services and other fronting:
Written1,688,098 1,266,878 (2,955,309)(333)1,397,382 433,981 (1,832,135)(772)
Earned1,515,059 364,115 (1,879,507)(333)1,290,675 233,792 (1,525,239)(772)
Consolidated:
Written$6,152,101 $2,500,428 $(4,141,713)$4,510,816 $5,652,484 $1,571,713 $(2,798,726)$4,425,471 
Earned$5,863,070 $1,171,545 $(2,829,889)$4,204,726 $5,287,875 $1,056,915 $(2,345,943)$3,998,847 
Substantially all of the premiums written and earned in the Company's program services and other fronting operations for the quarter and six months ended June 30, 2024 and 2023 were ceded. The percentage of consolidated ceded earned premiums to gross earned premiums was 43% and 40% for the quarter and six months ended June 30, 2024, respectively, and 38% and 37% for the quarter and six months ended June 30, 2023, respectively. The percentage of consolidated assumed earned premiums to net earned premiums was 32% and 28% for the quarter and six months ended June 30, 2024, respectively, and 29% and 26% for the quarter and six months ended June 30, 2023, respectively.

Substantially all of the incurred losses and loss adjustment expenses in the Company's program services and other fronting operations were ceded. These gross losses totaled $593.9 million and $1.2 billion for the quarter and six months ended June 30, 2024, respectively, and $594.7 million and $1.1 billion for the quarter and six months ended June 30, 2023, respectively.

The following table summarizes the effect of reinsurance and retrocessional reinsurance on losses and loss adjustment expenses in the Company's underwriting operations.

Quarter Ended June 30, Six Months Ended June 30,
(dollars in thousands)2024202320242023
Gross losses and loss adjustment expenses$1,577,820 $1,476,189 $3,271,667 $2,868,537 
Ceded losses and loss adjustment expenses(345,224)(288,676)(751,391)(507,931)
Net losses and loss adjustment expenses$1,232,596 $1,187,513 $2,520,276 $2,360,606