本文介绍生存模型,属于CS2第六章的内容,也是学习CM1的寿险精算部分的先修内容。
本文不仅适用于英国精算师的考试,Jackie 在写这篇推文时也参考了北美体系的内容,所以考SOA的同学也不妨看一下。
Notation
的分布
cdf of :
sf of :
pdf of :
Relationship between and
Events that are equivalent (important relationship between
的分布
cdf of :
sf of :
pdf of :
Chaining Survival
Conditions on
Assumptions on
The force of mortality
Typical curve for humans
- High infant mortality
- An ‘accident hump’ at ages around 20
- The nearly exponential increase at older ages
Some Common Mortality Models
- Exponential Model: Constant force of mortality
- De Moivre Model:
- Compertz Model
- Generalized (or Modified) De Moivre Model
Actuarial Notation
Survival:
Mortality:
Deferred Mortality:
It's convention that
3 ways to calculate
Relationship between F and f
Approximate with
For small
Distributional Quantities of
Mean of
Complete expectation of life:
Median of
This is the value
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