On the effectiveness of natural hedging for insurance companies and pension plans
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![Fig. 1. Central death rates of male assured lives, pensioners, and annuitants in UK, 1983-2006](https://thumb-us.123doks.com/thumbv2/123dok_us/1484214.101068/13.595.153.445.65.610/fig-central-death-rates-assured-lives-pensioners-annuitants.webp)
![Fig. 2. Parameter estimates of x,i (top), x,i (middle), and t,i (bottom) of cPLCM for assured lives](https://thumb-us.123doks.com/thumbv2/123dok_us/1484214.101068/14.595.149.436.78.518/fig-parameter-estimates-x-middle-cplcm-assured-lives.webp)
![Fig. 3. Parameter estimates of x,i (top), B or xx,i (middle), and K or tt,i (bottom) of PCFM for](https://thumb-us.123doks.com/thumbv2/123dok_us/1484214.101068/15.595.81.509.75.520/fig-parameter-estimates-top-middle-and-bottom-pcfm.webp)
![Fig. 4. Parameter estimates of (top), x jx (middle), and jt (bottom) of product model of](https://thumb-us.123doks.com/thumbv2/123dok_us/1484214.101068/16.595.78.510.77.515/fig-parameter-estimates-jx-middle-jt-product-model.webp)
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