(Reuters) - RenaissanceRe Holdings Ltd (RNR.N) will buy fellow Bermuda-based reinsurer Platinum Underwriters Holdings Ltd (PTP.N) for about $1.9 billion to boost its business amid intensifying competition and falling premiums.

RenaissanceRe will offer an equivalent of $76 per share in stock and cash, representing a 24 percent premium to Platinum's closing price of $61.27 on Friday.

Platinum's shares rose as much as 21 percent to $74.35 in morning trading.

Reinsurers such as RenaissanceRe and Platinum help insurance companies cover the cost of major damage claims, such as for hurricanes or earthquakes, in exchange for part of the premiums their customers pay.

But fewer natural catastrophes in recent quarters and a rise in competition from pension and hedge funds entering the industry in search of higher returns, have been reducing reinsurers' pricing power and pushing them to look at buying better products or expanding geographically.

"The declining pricing and a tougher market environment forced RenaissanceRe's hand," Macquarie analyst Amit Kumar said.

The offer price, which is at 1.1 times Platinum's book value, undervalues the company, Kumar said, adding that he expects other potential buyers to emerge.

Under the deal, Platinum's shareholders will get a $10-per-share special dividend, and will be able to choose the rest in the form of $66 in cash or 0.6504 in RenaissanceRe shares or a combination of $35.96 in cash and 0.2960 RenaissanceRe stock.

RenaissanceRe said it expected annual cost savings of $30 million from the deal, which is due to close in the first half of 2015. It will pay a break-up fee of $60 million if the deal fails to close, the company said on a conference call.

RenaissanceRe Chief Executive Kevin O'Donnell will head the combined company. Platinum CEO Michael Price will have no future role.

Morgan Stanley is the financial adviser to RenaissanceRe, while Goldman Sachs is advising Platinum.

Willkie Farr & Gallagher is legal counsel for RenaissanceRe, while Sullivan & Cromwell is advising Platinum.

Platinum shares were up 20.5 percent at $73.87, while Renaissance shares were down 2.1 percent at $99.32 at midday.

(Reporting by Avik Das and Anil D'Silva in Bangalore; Editing by Ted Kerr, Siddharth Cavale and Maju Samuel)