# Topic 4 RMI

## 29 terms

### Risk

Uncertainty; variation around expected loss vs actual loss

P* (P-star)

### Expected Loss

Core of risk management decision making.

### P*

Planned losses, expected losses, expected severity are variations around

### Exposure units

Things exposed to loss like cars, drivers, buildings, person's life are...

### P*

Basis for insurance pricing.

premium charged for insurance per exposure unit; must cover all costs of insurers; insurer does not know all the costs until the last claim is settled

Losses, expenses, administrative costs are covered by...

Amount of gross premium sufficient to pay for losses only (P*); must be an estimate so it can be wrong; if actual losses are equal to expected losses than they break even, it's AL<EL it's a profit and if AL>EL it's a loss

### Risk Charge

Reflects the estimation risk for an insurer; needed because P* is an estimate; it is the cushion for the risk incurred by insuring something

### Influences of risk charge

Accuracy of P, if confidence in P is high from lots of past data, small RC, if not confident in P* from little past data, high RC

### Probability

Measures the likelihood of an event (chance/odds); ranges from 0-1; if 0, the event is impossible, if 1, the event is certain

### Mutually exclusive

They cannot occur at the same time - individual probabilities must sum up to one

### Random Variables

Outcomes depends on some chance event, the results are random like rolling the dice, examples are frequency and severity

### Frequency

total number of losses in a given time period

### Severity

Dollar value of losses that do occur

### Probability Distribution

Graph or table which indicates for each outcome of a random event, the probability of that occurring; uniform distribution; bell curve

### Measure of central tendency

Mean = expected value = P*, median, and mode

### Mean calculation

1(1/6)+ 2(1/6)+ 3(1/6)+ 4(1/6)+ 5(1/6)+ 6(1/6)=3.5 (1-6 being the possible outcomes)

### Measure of dispersion

How to measure the measures of risk, measures frequency variance or standard deviation and coefficient of variation. Greater dispersion, greater the risk

### Law of large numbers

Overtime the data you collect or more observations that occur; your results will get close to the accurate result

### Frequency

Total number of accidents divided by total number of drivers

### Severity

Multiply # of accidents with particular loss amount by the loss amount and add up all the numbers and divide that by the total number of losses to get the total on average value of losses.

### Priori Probability

Can be deduced in advance, all outcomes are known, all outcomes are equally likely, all outcomes are mutually exclusive

### Statistical probability

Make estimates based on statistics; run an experiment and use results from collected data

### Maximum possible loss

Only one answer, the highest possible amount of loss that could occur

### Maximum probable loss

Largest loss that most likely would occur, not always an exact answer; key is how you present: 95% chance loss will be 1000 or less, true; 95% chance loss will be 1000, not true because the % that 1000 will occur is not 95%.