Ricerc@Sapienza

We investigate the application of natural hedging strategies for long-term care
(LTC) insurers by diversifying both longevity and disability risks affecting LTC
annuities. We propose two approaches to natural hedging: one built on a multivariate
duration, the other on the Conditional Value-at-Risk minimization of
the unexpected loss. Both the approaches are extended to the LTC insurance
using a multiple state framework. In order to represent the future evolution of
mortality and disability transition probabilities, we use the stochastic model of

In this paper, we propose a de-risking strategy model for LTC insurers facing with longevity and disability risks, by constructing hedge positions with vanilla disability swaps and options. We rely on long-term care insurance in a multiple state framework. The optimal hedge level for each de-risking strategies is computed, respectively, by minimizing the total cost of the de-risking strategy under the Conditional Value-at-Risk (CVaR) constraint on the total unfunded liabilities and minimizing the CVaR under a total cost constraint.