Abstract
This article aims at linking conceptually the default puts of (risk-neutral) optional finance to the safety loadings of (historical) actuarial theory that typically serve to reduce bankruptcy risk. We illustrate this study by detailing the contractual provisions underlying typical participating contracts (described and priced by Jørgensen [2001] or Bernard, Le Courtois and Quittard-Pinon [2005b], to quote only a few). Our analysis aims at extending and applying the ideas proposed by B¨uhlmann [2004], and is sequencing the famous and fundamental works of Merton [1974], Black and Cox [1976], Longstaff and Schwartz [1995]... Beyond the chosen examples, the ultimate goal of this work is to make understand and detail some links and similarities between contingent claims based pricing and standard actuarial safety loadings.