Chapter 0 and Chapter 1

Question 1

Define survival analysis

Answer 1

Study of the distirbution of lifetimes or time from some initating event to a terminal event - can be applied to study of distribution of times from changing one state to another

Question 2

Where are survival models used in actuarial

Answer 2

Life assurance
Annuties
Critical illness cover
Pension funds

Question 3

Why is the difference in actuarial vs statistical notation so important?

Answer 3

In survival models actuaries are interested in financial significance vs statisticians statistical significance - something can be acceptable under actuarial criteria but not statistically so its key we understand the purpose of the model

Question 4

Explain meaning of variable T

Answer 4

The future lifetime of a new born person is a random variable T which is continuously distirbuted over interval 0 to omega where omega is between 0 and infinity

Question 5

Explain limiting age

Answer 5

Denoted omega - usually 100 - 200 years old and is the oldest or max age to live to.

Question 6

Explain meaning of variable Tx

Answer 6

The future life of a person aged x is a random variable T describing future lifetime after age x of person who survives until age x. T0= T by convention

Question 7

What is the only distirbution function we need to find all Fx(t)

Answer 7

F0(t)

Question 8

What does tqx mean?

Answer 8

Rate of mortality : Probability of life age x dying before age x+t

Question 9

What does tpx mean?

Answer 9

Probability of life age x surviving next t years

Question 10

What does qx mean

Answer 10

Probability that a life alive at age x dies before age x+1

Question 11

What is the probability of surviving for time s+t after age x? in terms of multiplying two probabilities

Answer 11

Multiplying probability of surviving for time s after age x and probability of then surviving for a further time t at age x+s

Question 12

Desribe the force fo mortality in words

Answer 12

The instantaneous measure of mortality at age x - as in you’re alive at x but die instantly. This measure can be over 1 briefly for short periods of time

Question 13

Define the complete expectation of life

Answer 13

The complete expectation of life at age x is defined as E(Tx) which is the expected future lifetime after age x. Often it is used to measure countries’ standard of living however this average can be skewed so the median would be a better measure.

Question 14

Define the curtate expectation of life

Answer 14

Curtate expectation of life is the expectation of Kx random variable where Kx is age last birthday. IE E[Tx] - rounded down

Question 15

How can the Curtate expectation of life be an non integer value

Answer 15

It is average. although Kx has to be an integer the average of a collection of integers can be a decimal

Question 16

IF i have the force of mortality what can I work out about survival

Answer 16

Survival rates through lemma 5 or survival function

Question 17

Why is the exponential model with constant hazard not realistic for humans

Answer 17

Mortality rates are independent of age in this model - not true in reality

Question 18

How does the Weibull model relate to the exponential

Answer 18

If Beta = 1 then the hazard is constant and weibull model is the same as the exponential. However unlike exponential different values of beta alter the hazard to be monotonically increasing or decreasing with time

Question 19

Discuss Gompertz law

Answer 19

Says with age force of mortality goes up and keeps going up, its entirely driven by age. This is a reasonable assumption for middle to older age groups.

Question 20

Discuss makehams law

Answer 20

Includes a constant figure that can be interpreted as an allowance for accidental deaths not depending on age. - good approximation

Question 21

What are life tables

Answer 21

These are routinely published by the profession - they summarise the mortality experience of a certain group of lives. The tables are usually refreshed with each census and there are lots of different tables with different uses

Question 22

What does x denote int he tables

Answer 22

The exact age of the person on their last birthday

Question 23

What does lx denote int he tables

Answer 23

Number of people surviving to exact age x out of original 100k aged 0

Question 24

What does dx denote in the tables

Answer 24

number of deaths in year age x to x+1 out of the lx persons who enter that year

Question 25

What does Lx denote in the tables

Answer 25

Population to be expected according to the Life Table aged between x and x+1 years, assuming deaths occur evenly over the year

Question 26

What does Tx denote in the tablest

Answer 26

Expected number of person years to be lived byt eh survivors at age x

Question 27

What does e^ox denote in the tables

Answer 27

Life expectancy at age x for each person surviving, or total future lifetime in years which an average is passed through by people aged exactly x - period life expectancy

Question 28

Explain life expectancy

Answer 28

Average number of years a person would live if current mortality rates applied in the future.

Question 29

Explain the difference between period life expectancy and cohort life expectancy

Answer 29

Period life expectancy assumes mortality rates remain constant into the future, while cohort life expectancy uses projected changes in future mortality rates