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NATURAL HEDGING IN LONG-TERM CARE INSURANCE

Published online by Cambridge University Press:  13 September 2017

Susanna Levantesi  and
Massimiliano Menzietti
Susanna Levantesi*
Affiliation:
Department of Statistics, Sapienza University of Rome, Viale Regina Elena 295/G, 00161, Rome, Italy
Massimiliano Menzietti
Affiliation:
Department of Economics, Statistics and Finance, University of Calabria, Ponte Pietro Bucci, 87036, Campus of Arcavacata (Cosenza), Italy, E-mail: massimiliano.menzietti@unical.it
*
E-mail: susanna.levantesi@uniroma1.it
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Abstract

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.

Keywords

Long-term care insurancenatural hedgingdisability riskmultivariate durationconditional VaR minimization
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 233 - 274
Copyright
Copyright © Astin Bulletin 2017 

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