Life Insurance - C2-C3

If we deal with something uncertain =>

In order to estimate the time at which a death benefit is payable …

(x)

T_x

Lifetime Distribution

Survival Function

P(A|B) =

S_x(t) =

Any survival probability for (x), for, say, t + u years can be split into

Any survival function for a lifetime distribution must satisfy the following conditions to be valid:

limiting age = ω

For all the distributions used in this book, we make three additional assumptions:

Limiting age of model

Force of Mortality

What is it + Why we use it

Force of Mortality

Formulas + When to Use

PDF of death

Formula

Survival Function using Force of Mortality

The integral accumulates all the "death pressure" you face over the time interval, and the negative exponential turns that total pressure into a survival percentage.

Force of Mortality fully describes lifetime distribution.

Mortality Laws

Mortality Laws

Gompertz' Law

Mortality Laws

Makeham's Law

Mortality Laws

Makeham's Law

Constants Elaboration

Theoretical Laws

Actuarial Notation

Force of Mortality μ_x Relationships

with survival function and density

Mortality Rate: Integral Representation

Complete Expectation of Life

Term Expectation of Life

Curtate Future Lifetime K_x

Curtate Expectation of Life

Variance of K_x

Leibniz Integral rule

Geometric Series

Chapter 3: Life Tables and Selection

A life table is a summary of a survival model, usually tabulated at integer ages only.

l_x0

l_x

d_x

Fractional Age Assumptions

Multiplication Rule for Survival Probabilities

Uniform Distribution of Deaths (UDD)

MEMORISE

Uniform Distribution of Deaths (UDD)

Recognize & Understand the Trap

Constant Force of Mortality (CFM)

Constant Force of Mortality (CFM)

Comparison

National Life Tables

Properties

Mortality for insured lives differs from non-insured, why?

Life Insurance Underwriting

Select and Ultimate Survival Models

Notations

if t ≥ d

Constructing Select Life Tables

Constructing Select Life Tables

2

Does Selection always mean Lower Mortality?

Heterogeneity & Adverse Selection