Convex Insurance | 29,302 followers on LinkedIn. Convex is an international specialty insurer and reinsurer founded by Stephen Catlin and Paul Brand | Convex is a stimulating environment that offers the opportunity to do something different, bringing together a seasoned team with specialist underwriting capabilities, at the forefront of their respective disciplines. With no legacy systems to be maintained and a clean balance sheet, we have a strong focus on using modern technology specifically designed.