Practice Problems Help Set 2

Front 1

Normal TVaR shortcut

Back 1

u + σ[(Φ(Ζp)/(1-p]

Where Φ(Zp) = (1/sqrt(2pi))•e^-((x^2)/2

Front 2

Lognormal TVaR

Back 2

EX•[Φ(σ-zp)/(1-p)

Where Φ is just Z(x)

Front 3

For Bayesian estimate of the expected number of claims and other expected values, what do you have to multiply the posterior distribution by?

Back 3

The expected value

Front 4

Formula for indicated relativity?

Back 4

1-LER

Front 5

What is the indicated relativity for a deductible of 2 times the basic level deductible b for X~ Exponential(θ)?

Back 5

(EX-E[X^2b])/(EX-E[X^b])

(It’s the continuous version of 1-LER)

Front 6

Cov[Xi,Xj] = ? if i is not equal to j

Back 6

Cov[Xi,Xj] = a

Front 7

What is another name for the unconditional variance of X

Back 7

VarX

Front 8

In terms of Buhlmann credibility , Total Variance = ?

Back 8

v+a

Front 9

For finding the written premium for a calendar year, what’s the strategy to solve?

Back 9

Only add up the written premiums for the policies that were written in the calendar year (they started in the given calendar year)

(Also remember that written premium = earned premium + unearned premium)- so we don’t have to do any multiplication

Front 10

u is what in the ultimate formula for insurance?

Back 10

The policy limit (not the maximum covered loss, so be very careful here)

Front 11

What is the formula for the maximum covered loss, m?

Back 11

u/α + d

Be very careful not to mix the policy limit and maximum covered loss up

Front 12

PGF formula

Back 12

E[z^X] like E[2^n]

So anytime you see something with E[2^N] think Poisson PGF

Poisson PGF = e^λ(t-1)

Front 13

Variance of the Payments Per Loss

Back 13

E[(X^u]^2] - (E[X^u])^2

Front 14

First formula for the expected value of a policy limit, E[(X-u)]?

Back 14

Integral of x•f(x) from 0 to u + u• S(u)

Follows naturally from the Payment per loss with a policy limit Y^L

Front 15

2nd formula for E[(X-u)^k]

(Uses survival function)

Back 15

Integral of S(x) from 0 to u

Front 16

Expected value of a bonus formula

Back 16

u- E[(X^u)]

(If there is a constant, just pull it out)

Front 17

Expected value of a bonus B, EB if B= 500,000(0.7-R)/(3)

Back 17

(1/3)• 350,000- E[X^350,000]

Front 18

Which method for selecting loss development factors results in the highest reserve? All-year arithmetic average, 3 year arithmetic average, 2 year arithmetic average, or 1 year arithmetic average?

Back 18

All year arithmetic average

(This is always true, so no calculations are needed)

Front 19

Which results in a higher reserve, the All year arithmetic average, or the volume weighted average method?

Back 19

You have to calculate them both, but in that one problem the volume weighted average resulted in higher reserves

Front 20

True or False?

If X

Back 20

False

Front 21

True or False? If X

Back 21

True

Front 22

How do you solve for p in this equation? Z((1+p)/2))=1.28

Back 22

Find Z(1.28) from the Z table (=0.8997)

Then solve for p in this equation

(p+1)/2= 0.8997

Front 23

Log likelihood for the Weibull distribution with parameters t and θ with n number of losses? (use for likelihood ratio test)

Back 23

nln(t) - ntln(θ) + (t-1)• Σln(Xi) - θ^-t • ΣXi^t

Front 24

SFP covers direct loss from fire and lighting, plus at least one of the following coverages?

Back 24

• Personal coverage, such as for dwellings

• Commercial Coverage, such as general property and multiple locations

• Increased covered perils, such as extended coverage for perils of vandalism or malicious mischief

• Increased covered loss, such as additional living expenses, rental value, rental income, leasehold interests, demolition expenses, consequential loss or damage, replacement costs, business interruption losses, profits and commissions losses, and extra expenses

Front 25

Formula for ILF

Back 25

LAS(u)/LAS(b)

u is the increased limit, b is the increased limit

Front 26

When they say penalized log likelihood they mean find what?

Back 26

The AIC or SBC/BIC

Front 27

When they say continuously compounded, use what?

Back 27

Use e

Front 28

When they say annual compounded rate, use what?

Back 28

(1+i) ^ t

Front 29

Formula for losses incurred to date

Back 29

Losses Paid to Date + case reserves

Front 30

What do you multiply the incurred losses paid to date by to develop to ultimate losses?

Back 30

Use the incurred loss factors (not the paid loss factors)

Hint 30

A

Front 31

The insurance company expects 1000 claims per year. The company reinsured the layer of loss from 2,000 to 10,000 with a reinsurance company. Calculate the expected payment per year for the reinsurance company as a result of the claims from the insurance company

Back 31

Solve this equation:

1000[E(X^10,000) - E[(X^2,000)]

Front 32

Quota share treaty

Back 32

A reinsurance company will pay for a portion of the total losses

Front 33

Surplus share reinsurance

Back 33

A reinsurance company pays for a portion of the losses greater than the retention limit + the retention limit

Front 34

For the alternate method, do you do frequency and severity together or separately?

Back 34

Do them separately (so do the loss development factors separately before combining)

Front 35

Closure rate

Back 35

# of closed claims/ # of open claims

Front 36

Formula for probability within an interval using Survival functions

Back 36

S(a) - S(b)

Front 37

Probability of an interval using CDF’s

Back 37

F(b)- F(a)

Front 38

Are rehabilitative and habilitative services and devices an essential benefit under the ACA?

Back 38

Yes, they are an essential benefit.

Front 39

Are mental health and substance use disorder services an essential benefit under the ACA?

Back 39

Yes, they are an essential benefit under the ACA

Front 40

For aggregate probabilities, when do you multiply by 2?

Back 40

When the amounts are different.

Ex: 2• P(X=3)•P(X=4)

But when the amounts are the same you don’t multiply by 2

Ex: P(X=3)• P(X=3)

Front 41

True or False: The chain- ladder method is often used on a new line of business?

Back 41

False

But the expected loss ratio is often used on a new line of business since it does not require claims experience

Front 42

True or False: the expected loss ratio will always produce a larger reserve than the chain- ladder method?

Back 42

False

Front 43

For data preparation for ratemaking, we always assume uniformly written policies are issued at the what of the month?

Back 43

Midpoint