(Adds details on claims, Brexit, insurance lines)
Nov 8 (Reuters) - Lloyds Of London insurer Beazley Plc reported an 11.1 percent rise in gross written premiums for the first nine months of 2018, helped by growth across all its divisions, and said it would report high single-digit growth in premiums for 2019.
However, the company, which is a part of the oldest insurance market in the world, estimated the initial cost of the recent Atlantic hurricanes and the typhoons in Asia to be around $105 million.
Although still substantial, the claims compared with a natural catastrophe bill between $200 million and $300 million from natural catastrophes in the second half of 2017.
"Our business continues to deliver double-digit premium growth and has been aided by higher rates in some classes following last year's catastrophe losses," said Andrew Horton, Beazley's chief executive officer, in a statement.
The industry had faced record insurance losses of more than $135 billion from hurricanes, earthquakes and wildfires last year.
Beazley said it would stop underwriting construction and engineering business, a unit that accounted for about 10 percent of its property division's premiums in 2017.
"After careful analysis, we concluded it (construction and engineering business) was unlikely to satisfy our cross-cycle profitability requirements in the foreseeable future," the company said.
The company, which focuses on insurance lines such as data breach, management liability and healthcare, said gross written premiums rose to $1.96 billion for the nine months ended Sept. 30, from $1.76 billion a year earlier.
Beazley, which had warned in July that a "hard" Brexit could prove very expensive for Britain's insurance sector, said on Thursday that it was working with Lloyd's to ensure a smooth transition for its customers in all Brexit outcomes.
Reporting by Muvija M and Noor Zainab Hussain in Bengaluru; Editing by Gopakumar Warrier