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Reinsurance (Tables)
 9 Months Ended
Sep. 30, 2018
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Abstract]  
Effect of Reinsurance and Retrocessional Activity on Premiums Written and Earned and on Net Claims and Claim Expenses Incurred
The following table sets forth the effect of reinsurance and retrocessional activity on premiums written and earned and on net claims and claim expenses incurred:
 
 
 
 
 
 
 
 
 
 
 
 
Three months ended
 
Nine months ended
 
 
 
September 30,
2018
 
September 30,
2017
 
September 30,
2018
 
September 30,
2017
 
 
Premiums written
 
 
 
 
 
 
 
 
 
Direct
$
74,635

 
$
64,040

 
$
250,375

 
$
205,253

 
 
Assumed
551,042

 
576,229

 
2,512,297

 
2,184,521

 
 
Ceded
(172,422
)
 
(157,048
)
 
(1,041,864
)
 
(806,672
)
 
 
Net premiums written
$
453,255

 
$
483,221

 
$
1,720,808

 
$
1,583,102

 
 
Premiums earned
 
 
 
 
 
 
 
 
 
Direct
$
73,356

 
$
61,908

 
$
213,292

 
$
176,433

 
 
Assumed
760,920

 
712,499

 
1,968,138

 
1,731,845

 
 
Ceded
(302,427
)
 
(226,615
)
 
(779,914
)
 
(612,176
)
 
 
Net premiums earned
$
531,849

 
$
547,792

 
$
1,401,516

 
$
1,296,102

 
 
Claims and claim expenses
 
 
 
 
 
 
 
 
 
Gross claims and claim expenses incurred
$
514,873

 
$
2,482,510

 
$
817,560

 
$
2,924,217

 
 
Claims and claim expenses recovered
(104,363
)
 
(1,260,814
)
 
(175,180
)
 
(1,366,853
)
 
 
Net claims and claim expenses incurred
$
410,510

 
$
1,221,696

 
$
642,380

 
$
1,557,364