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Download Actuarial mathematics for life contingent risks by D C M Dickson; Mary Hardy; H R Waters PDF

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By D C M Dickson; Mary Hardy; H R Waters

Balancing rigour and instinct, and emphasizing functions, this contemporary textual content is perfect for collage classes and actuarial examination preparation.

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When the employee leaves or retires, the proceeds are available to provide income throughout retirement. In the UK most of the proceeds must be converted to an annuity. In the USA and Canada there are more options – the pensioner may draw funds to live on without necessarily purchasing an annuity from an insurance company. 2 Defined benefit pension design The age retirement pension described in the section above defines the pension payable from retirement in a standard final salary plan. Career average salary plans are also common in some jurisdictions, where the benefit formula is the same as the final salary formula above, except that the average salary over the employee’s entire career is used in place of the final salary.

Now, we can sum over all the possible death intervals s to s + ds – which requires integrating because these are infinitesimal intervals – to obtain the probability of death before age x + t. 3. This type of interpretation is important as it can be applied to more complicated situations, and we will employ the time-line again in later chapters. 20) becomes 1 qx = s px µx+s ds. 0 When qx is small, it follows that px is close to 1, and hence s px is close to 1 for 0 ≤ s < 1. Thus 1 qx ≈ µx+s ds ≈ µx+1/2 , 0 where the second relationship follows by the mid-point rule for numerical integration.

Now, we can sum over all the possible death intervals s to s + ds – which requires integrating because these are infinitesimal intervals – to obtain the probability of death before age x + t. 3. This type of interpretation is important as it can be applied to more complicated situations, and we will employ the time-line again in later chapters. 20) becomes 1 qx = s px µx+s ds. 0 When qx is small, it follows that px is close to 1, and hence s px is close to 1 for 0 ≤ s < 1. Thus 1 qx ≈ µx+s ds ≈ µx+1/2 , 0 where the second relationship follows by the mid-point rule for numerical integration.

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