Protection of a Company Issuing a Certain Class of Participating Policies in a Complete Market Framework

In this article, we examine to what extent policyholders buying a certain class of partici- pating contracts (in which they are entitled to receive dividends from the insurer) can be described as standard bondholders. Our analysis extends the ideas of Bühlmann [2004], and sequences the fundamental advances of Merton [1974], Longstaff and Schwartz [1995], and Briys and de Varenne [1994, 2001]. In particular, we develop a setup where these
participating policies are comparable to hybrid bonds but not to standard risky bonds (as done in most papers dealing with the pricing of participating contracts). In this mixed framework, policyholders are only partly protected against default consequences. Continu- ous and discrete protections are also studied in an early default Black and Cox [1976] type setting. A comparative analysis of the impact of various protection schemes on ruin prob- abilities and severities of a Life Insurance company which only sells this class of contracts concludes this work.