Natural hedging in long-Term care insurance
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
Cairns et al. (2009) with cohort effect under parameter uncertainty through a
semi-parametric bootstrap procedure. We calculate the optimal level of a product
mix and measure the effectiveness provided by the interaction of LTC stand
alone, deferred annuity and whole-life insurance. We compare the results obtained
by the two approaches and find that a natural hedging strategy for LTC
insurers is attainable with a product mix of LTC and annuities, but including
low proportion of LTC.
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