## Natural hedges with immunization strategies of mortality and interest rates.(English)Zbl 1431.91339

Summary: In this paper, we first derive closed-form formulas for mortality-interest durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel movement, respectively, in $$\mu^*$$ (the force of mortality-interest), the addition of $$\mu$$ (the force of mortality) and $$\delta$$ (the force of interest). We then build several mortality-interest duration and convexity matching strategies to determine the weights of whole life insurance and deferred whole life annuity products in a portfolio and evaluate the value at risk and the hedge effectiveness of the weighted portfolio surplus at time zero. Numerical illustrations show that using the mortality-interest duration and convexity matching strategies with respect to an instantaneously proportional change in $$\mu^*$$ can more effectively hedge the longevity risk and interest rate risk embedded in the deferred whole life annuity products than using the mortality-only duration and convexity matching strategies with respect to an instantaneously proportional shift or an instantaneously constant movement in $$\mu$$ only.

### MSC:

 91G05 Actuarial mathematics 91G30 Interest rates, asset pricing, etc. (stochastic models)
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### References:

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