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Stochastic Portfolio Specific Mortality and the Quantification of Mortality Basis Risk

Richard Plat

The last decennium a vast literature on stochastic mortality models has been
developed. However, these models are often not directly applicable to
insurance portfolios because:
a) For insurers and pension funds it is more relevant to model mortality
rates measured in insured amounts instead of measured in number of policies.
b) Often there is not enough insurance portfolio specific mortality data
available to fit such stochastic mortality models reliably.

Therefore, in this paper a stochastic model is proposed for portfolio specific
mortality experience. Combining this stochastic process with a stochastic country
population mortality process leads to stochastic portfolio specific mortality rates,
measured in insured amounts. The proposed stochastic process is applied to two
insurance portfolios, and the impact on the Value at Risk for longevity risk is
quantified. Furthermore, the model can be used to quantify the basis risk that remains
when hedging portfolio specific mortality risk with instruments of which the payoff
depends on population mortality rates.

Keywords: portfolio specific mortality, stochastic mortality models, mortality basis risk,
longevity risk, Solvency 2