Chaucer plans to raise £39m by selling shares through placings and open offers.
Investors will be able to buy two new shares for every three they already hold and will also have the chance to buy 19 units of loan stock for every 88 shares they currently hold.
The new shares will go on sale at 30.75p each.
The company's existing stock was trading at 33p on Tuesday, having been stable at 33.5p for several days.
The new shares have been conditionally placed with institutional investors.
Managing director Ewen Gilmour said Chaucer would use the cash to boost capacity by £40m on Syndicate 1096 and increase the group's funds at Lloyd's in support of its planned £210m interest next year.
It would also enable Chaucer to take advantage of high prices for insurance and reinsurance, Gilmour said.
The placings and open offers are underwritten by Numis Securities.