Katrín Pétursdóttir knows what treasure lies in the pile of skinned fish carcasses before her, and the investment needed to extract it. Seventy years ago her grandfather founded LÝSI, a fish processing company, which last year produced 6,000 tons of fish oil and $30 million in revenues with just 100 employees. In 2005, Pétursdóttir built a gleaming $4 million factory, and she has plans for a $7 million expansion to keep up with the growing demand among health-minded consumers for omega-3 fatty acids. But financing these ambitious plans may prove problematic, with Iceland mired in its first recession since 1992 and...