Minimum Return Rate Guarantees under Default Risk - Optimal Design of Quantile Guarantees

The paper analyzes the design of participating life insurance contracts with minimum return rate guarantees. Without default risk, the insured receives the maximum of a guaranteed rate and a participation in the investment... [ view full abstract ]

The paper analyzes the design of participating life insurance contracts with minimum return rate guarantees. Without default risk, the insured receives the maximum of a guaranteed rate and a participation in the investment returns. With default risk,  the payoff is modified by a default put implying a compound option. We represent  the yearly returns of the liabilities by a portfolio of plain vanilla options.
In a BS model, the optimal payoff constrained by a maximal shortfall probability can be stated in closed form. Due to the completeness of the market, it can be implemented for any equity to debt ratio.