SVB boss Matthew Fosh is drawing up plans to persuade investors to back a capital raising.
But the chief executive admitted he needed a "cogent, credible strategy" to win the battle for more cash.
Fosh took over at the troubled Lloyd's insurer after a period of heavy losses. The company has been notable for failing to raise new capital, while many of its competitors issued new shares.
"This year I would love to be able to come up with a strategy to persuade shareholders that we're worth it," he said. "No one's going to back us without the management - me - coming up with persuasive reasons why they should do so."
