(Reuters) -Australia's AUB Group ( AUBBF ) said on Tuesday it had granted Swedish private equity EQT exclusive access to its books after receiving a takeover offer which values the insurance broking company at A$5.25 billion ($3.41 billion). 

Under the proposal, EQT is offering A$45 per AUB share, which reflects a 25.1% premium to the Australian company's last close. 

Shares in the firm rallied to a record high, gaining as much as 11% to A$39.95. The stock was still trading lower than the offer price.

The A$45 apiece offer follows a previous approach, where the buyer had bid A$43 per share in cash.

The company said it had entered a confidentiality and exclusivity agreement with EQT and has provided the private equity firm access to its books for a six-week period, which began on October 8.

The news comes as AUB Group's ( AUBBF ) shares have largely stagnated over the past year despite steady institutional interest, underperforming both its rival, Steadfast Group ( SFGLF ), and the broader market.

AUB paused trading on Monday after the stock jumped more than 12%, saying it would respond to media reports and the sharp rise in its share price.

The deal is on the heels of AUB continuing to adjust to changes in its shareholder base, following U.S. private equity firm Odyssey Investment Partners' near A$277 million sell-down last year. 

The company currently counts First Sentier Investors and Capital World Investors as its top two shareholders, according to data compiled by LSEG.

Global firms and private equity investors have been active buyers in Australia, betting on steady premium growth and resilient cash flows even in volatile markets. 

"With organic opportunities for brokers moderating and brokers well capitalised following a firm pricing market, we would not be surprised if M&A continued to feature in the broking landscape," analysts at Jarden said in a note before the announcement.

EQT is a name known for its acquisitions, having very recently looked at Perpetual's wealth and corporate trust business.   

($1 = 1.5389 Australian dollars)