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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5092 . Since we know under this model that all lives will die before age 120, it makes sense that the uncertainty in the future lifetime should be greater for younger lives than for older lives. 6 is that we can obtain formulae for ◦ quantities of interest such as ex , but for many models this is not possible. For example, when we model mortality using Gompertz’ law, there is no explicit ◦ formula for ex and we must use numerical integration to calculate moments of Tx . In Appendix B we describe in detail how to do this.
The insurer is owned by the with-proﬁt policyholders. All proﬁts are distributed to the with-proﬁt policyholders through dividends or bonuses. A proprietary insurance company has shareholders, and usually has withproﬁt policyholders as well. The participating policyholders are not owners, but have a speciﬁed right to some of the proﬁts. Thus, in a proprietary insurer, the proﬁts must be shared in some predetermined proportion, between the shareholders and the with-proﬁt policyholders. Many early life insurance companies were formed as mutual companies.
E. membership of the pension plan), and with pensionable salary averaging S in, say, the ﬁnal three years of employment. A typical ﬁnal salary plan might offer an annual pension at retirement of B = Snα, where α is called the accrual rate, and is usually around 1%–2%. The formula may be interpreted as a pension beneﬁt of, say, 2% of the ﬁnal average salary for each year of service. The deﬁned beneﬁt is funded by contributions paid by the employer and (usually) the employee over the working lifetime of the employee.
Actuarial mathematics for life contingent risks by D C M Dickson; Mary Hardy; H R Waters