Siewert

Question 1

Advantages of high deductible plans (5)

Answer 1

1. achieves price flexibility while passing additional risk to larger insureds
2. reduced residual market charges and premium taxes
3. cash flow advantages for the insured (b/c insurer pays first)
4. provides incentive for insureds to control losses while providing large loss protection
5. allows “self-insurance” without rigorous state requirements

Question 2

Per aggregate XS losses under the LR approach

Answer 2

per aggregate XS loss = P * E * (1 - chi) * phi

P = Premium
E = ELR

chi = occurrence charge
this is the % of total losses XS of the deductible

phi = aggregate charge
this is losses in the deductible layer that exceed the aggregate

Question 3

Advantages of the LR approach to estimating XS losses (3)

Answer 3

1. can be used with no/immature data
2. LR estimate can be consistently tied to pricing programs
3. relies on a more credible pool of company and industry experience

Question 4

Disadvantage of the LR approach to estimating XS losses

Answer 4

ignores actual experience (less useful for mature AYs)

Question 5

Reason limits should be indexed for inflation

Answer 5

it keeps the proportion of deductible / excess losses consistent over time

otherwise, historical losses take too long to hit the deductible limit and distorts LDFs

Question 6

Advantages of the implied development approach to estimating XS losses (2)

Answer 6

1. provides estimate of XS losses at early maturities, even if no losses have yet emerged
2. limited LDFs are more stable than unlimited

Question 7

Disadvantage of the implied development approach for estimating XS losses

Answer 7

does not explicitly recognize XS loss development

Question 8

Limited tail factor formula using an inverse power curve

Answer 8

age-to-age factor = 1 + a * (t + c) ^ -b

t is the starting age in years

Question 9

Advantage and disadvantage of using an inverse power curve for the limited tail factor selection

Answer 9

advantage: produces uniformly decreasing tail factors that are consistent for each limit
disadvantage: bias exists because each limit is extended to the same maturity

Question 10

direct development approach - relationship of LDF and Limited LDF

Answer 10

LDF(L,t) = LDF(t) * R(L) / R(L,t)

(t) = LDF at age t
(L,t) = limited at L at age t
(L) = limited at L at ultimate

Question 11

XS LDF under the direct development approach for estimating XS losses

Answer 11

XSLDF(L,t) = LDF(t) * (1 - R(L))/(1-R(L,t))

(L,t) = limited at L at age t
(L) = limit at L at ultimate
(t) = unlimited at age t

Question 12

Weighted average form of the direct development approach

Answer 12

LDF(t) = R(L,t) * LDF(L,t) + (1 - R(L,t)) * XSLDF(L,t)

(t) = unlimited at time t
(L,t) = limited at L at time t
(L) = limited at ultimate

Question 13

Advantages of the direct development approach for estimating XS losses (2)

Answer 13

1. explicitly recognizes excess development
2. ensures consistency between limited and excess LDFs

Question 14

Disadvantages of the direct development approach for estimating XS losses (2)

Answer 14

1. XS LDFs tend to be volatile and overly leveraged
2. over/under estimates reserves at early ages

Question 15

Credibility weighting/BF method for estimating XS losses

Answer 15

L = Ot * LDFt * Z + E * (1 - Z)

when Z = 1/LDFt then this equals BF method

becomes paid to date + E * % unpaid

Question 16

Advantages of the credibility weighting/BF method for estimating XS losses (3)

Answer 16

1. liabilities can be determined directly or indirectly
2. ability to tie into pricing estimates for immature years with no loss experience
3. produces more stable estimates over time

Question 17

Disadvantage of the credibility weighting/BF method for estimating XS losses

Answer 17

ignores actual experience to the extent of the complement of credibility