A211 - Financial Mathematics > Chapter 1 > Flashcards

Chapter 1 Flashcards

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1
Q

If the interest rate is a lognormal random variable, what are its parameters?

A

m and s.

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2
Q

What must be developed to build a model of a system or process?

A

A set of mathematical or logical assumptions about how it works.

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3
Q

What determines the complexity of a model?

A

The complexity of the relationships between the various model parameters.

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4
Q

Name some factors that must be considered when modeling a life office.

A
  • Regulations
  • Taxation
  • Cancellation terms
  • Future events affecting investment returns
  • Inflation
  • New business
  • Lapses
  • Mortality
  • Expenses
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5
Q

What is a cancellation in insurance terms?

A

A cancellation occurs when a policyholder terminates their insurance cover

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6
Q

What is a lapse in insurance terms?

A

A lapse occurs when a policyholder doesn’t pay a premium that is due

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7
Q

What types of data need to be considered for modeling in insurance?

A

Data from past observations, current observations, and expectations of future changes

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8
Q

Give an example of a future change in insurance context.

A

An increase in the rate of insurance tax by the government

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9
Q

What statistical methods can be used when observed data are suitable for modeling?

A

Statistical methods to fit the data

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10
Q

What parameters are used to model daily changes in the price of shares?

A

The mean and the variance

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11
Q

How can the mean and variance be estimated?

A

By looking at past data and calculating the sample mean and sample variance

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12
Q

What should be considered before finalizing the choice of model and parameters?

A

The objectives for creation and use of the model

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13
Q

In insurance modeling, what may take precedence over creating the most accurate model?

A

Creating a model that will not understate costs or other risks

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14
Q

What is a key consideration when choosing between probability distributions for modeling claims?

A

How well the distribution models both small and large claims

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15
Q

How does a poor model of higher claims affect a company?

A

It may result in more costly decisions despite being slightly inaccurate on small claims

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16
Q

Do actuaries follow a rigid pattern of steps in the modeling process?

A

No, they move back and forth between key steps continuously

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17
Q

What is the purpose of introducing key steps in the modeling process?

A

To help understand the topic of modeling in insurance

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18
Q

Fill in the blank: A _______ occurs when a policyholder terminates their insurance cover.

A

cancellation

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19
Q

Fill in the blank: A _______ occurs when a policyholder doesn’t pay a premium that is due.

A

lapse

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20
Q

What is an example objective when modelling insurance claims?

A

Give as accurate a prediction as possible for 95% of the claims

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21
Q

What does model validation involve?

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A

A series of diagnostic tests to ensure that the model meets the objectives

22
Q

What should be done after defining the model?

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A

Refine the level of detail in the model at a later stage

23
Q

Why is it important to involve experts in the modelling process?

Study These Flashcards
A

To get feedback on the validity of the conceptual model

24
Q

What should be chosen for the implementation of the model?

Study These Flashcards
A

A statistically reliable random number generator

25
What is sensitivity testing?
A procedure to use a range of values for input parameters to assess model output
26
What is one of the most important benefits of modelling in actuarial work?
It allows studying systems with long time frames in compressed time ## Footnote For example, the operation of a pension fund can be analyzed more efficiently through modelling.
27
What is a key advantage of simulation modelling in the context of life insurance?
It helps study the operation of a life insurance company, which cannot be easily described by traditional mathematical models ## Footnote This is particularly relevant for complex systems with stochastic elements.
28
What can be compared using different future policies in a model?
Different policies or possible actions to determine which best suits user requirements or constraints
29
How can variance of results be controlled in a complex system model?
By controlling the experimental conditions to reduce variance without affecting mean values
30
What is a disadvantage of models in actuarial contexts?
Model development requires considerable investment of time and expertise ## Footnote This includes financial costs associated with validating assumptions and interpreting results.
31
What is a challenge associated with interpreting model outputs?
The need to communicate results effectively to a target audience ## Footnote The audience may include policyholders, pension fund clients, and finance directors.
32
Who might be a target audience for actuarial model outputs?
Examples include: * A life office policyholder * A pension fund client * The finance director of a general insurance company
33
What does a life office policyholder want to know from a model?
How much will be received from a particular policy when it matures
34
What is one of the most important benefits of modelling in actuarial work?
It allows studying systems with long time frames in compressed time ## Footnote For example, the operation of a pension fund can be analyzed more efficiently through modelling.
35
What is a key advantage of simulation modelling in the context of life insurance?
It helps study the operation of a life insurance company, which cannot be easily described by traditional mathematical models ## Footnote This is particularly relevant for complex systems with stochastic elements.
36
Why must randomness be included in a model?
To obtain meaningful results when randomness is an essential part of the process ## Footnote This enhances the accuracy and relevance of the model's outputs.
37
What can be compared using different future policies in a model?
Different policies or possible actions to determine which best suits user requirements or constraints
38
How can variance of results be controlled in a complex system model?
By controlling the experimental conditions to reduce variance without affecting mean values
39
What is a disadvantage of models in actuarial contexts?
Model development requires considerable investment of time and expertise ## Footnote This includes financial costs associated with validating assumptions and interpreting results.
40
What is a challenge associated with interpreting model outputs?
The need to communicate results effectively to a target audience ## Footnote The audience may include policyholders, pension fund clients, and finance directors.
41
Who might be a target audience for actuarial model outputs?
Examples include: * A life office policyholder * A pension fund client * The finance director of a general insurance company
42
What does a life office policyholder want to know from a model?
How much will be received from a particular policy when it matures
43
What information does a pension fund client require from a model?
How much to pay into the company’s pension fund next year
44
What does a finance director of a general insurance company want to estimate from a model?
The end-of-year profit figures
45
How does the output of a deterministic model behave?
The output is determined once the set of fixed inputs and the relationships between them have been defined. ## Footnote This means that for the same inputs, the output will always be the same.
46
How does the output of a stochastic model behave?
The output is random in nature, similar to the random variables of the inputs. ## Footnote This randomness means outputs can vary even with the same set of inputs.
47
What is required to study the implications of a stochastic model?
Several independent runs for each set of inputs. ## Footnote This approach allows statistical theory to be applied in understanding the model's behavior.
48
In what way is a deterministic model a special case of a stochastic model?
A deterministic model is a simplified case where there are no random components. ## Footnote This relationship highlights that all deterministic models can be viewed as stochastic models under specific conditions.
49
Fill in the blank: The output of a _______ model is determined by fixed inputs.
deterministic
50
True or False: A stochastic model produces the same output for the same set of inputs.
False
A211 - Financial Mathematics
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