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

Abstract

In this article we examine to what extent policyholders buying a certain class of participating 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 and sequences the fundamental advances of Merton, Longstaff and Schwartz, and Briys and de Varenne. 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. Continuous and discrete protections are also studied in an early default Black and Cox-type setting. A comparative analysis of the impact of various protection schemes on ruin probabilities and severities of a life insurance company that sells only this class of contracts concludes this work.

Optimal investment strategies for participating contracts

“…Instead, when the terminal portfolio value X π T is smaller than the guaranteed amount, the policyholder is only entitled to the portfolio value. In contrast, following the work by Bernard et al [3], we also investigate the fully protected participating contract that entitles the policyholder to a payoff as follows:…”

“…The payoff structures for the defaultable and protected policies, Ψ(x) and Ψ(x), are given in (3) and (5). With U (•) given by ( 6), U [Ψ(x)] zero for x L T g , and concave for x L T g , while U [ Ψ(x)] is convex when x < L g T and concave for x ≥ L g T .…”

“…which have longer maturities than standard options. This is examined in Bernard and Le Courtois [2] and Bernard et al [3].…”

“…Moreover, decision-makers are taken to be risk averse with respect to gains and risk seeking with respect to losses, which results in a S-shaped power utility function. This utility function is exploited in our problem to reflect this behavioral perspective for the insurance company, which plays the role of the asset manager, to derive explicit optimal investment strategies for two participating contracts with point-to-point basis guarantees, which we call (following Bernard et al [3]) the defaultable participating contract and the fully protected participating contract. The solutions provide insights for the insurance company in constructing portfolios to serve its purposes.…”