B6. Aggregate Excess Lost Cost Estimation

Question 1

How to build Table M

6 columns

Answer 1

1. Claim Amount ($) = start at 0, end with max
2. # of claims
3. Entry Ratio (r) = Claim Amount / Average Claim Amount
4. # and % of claims above claim amount
5. Φ(r) = Φ(r+1)+(r+1-r)(% claims above r)
6. Ψ(r) = Φ(r) + r - 1

Question 2

E[L] / Net Insurance Charge (I)

E[Ratable Loss] for Regular Table M

Answer 2

E[L] / E[A] = 1 + savings(h) - charge(g)
E[L] = E[A] - [charge(g) - savings(h)]E[A] = E[A] - I
* where I = [charge(g) - savings(h)]E[A]
* where r = Actual Loss / Expected Loss = A/E[A]

Question 3

Regular Table M

E[R] / GCP / Expense Component of Basic Premium

When are they =?

Answer 3

Equal in a balanced retrospective plan:
E[R] = (B+c(E[A] - I))T
GCP = (e+E[A])T
* where e = total expenses and profit (not in T)

Solve for B = e-(c-1)E[A] + cI
Expense component: e-(c-1)E[A]

Question 4

Table M / Limited Table M / Table L

Φ(rH) - Φ(rG) / rG -rH

Answer 4

charge(rH) - charge(rG) = (e+E[A])T - H / cE[A]T
rG -rH = G-H / cE[A]T

charge(rH) - charge(rG) = (e+E[A])T - H / cE[Ad]T
rG -rH = G-H / cE[Ad]T

Table M formula same as Table L

Question 5

Calculate Insurance Charge (Vertically)

What about for Table L

Answer 5

1. Loss
2. Entry Ratio (r)
3. Excess of r (min 0)
4. Charge = sum(excess of r) / n
5. Table L Charge = sum(excess of r) / n + k

Question 6

Limited Table M

Entry Ratio (r)

What about for deductible (per occurance and aggregate)?

Answer 6

r = Ad / E[Ad]
E[Ad] = (1-k)E[A]
* where k = XS Ratio

r = Agg Deductible Limit / E[Ad]
* where E[Ad] = (1-k)*E[A]

Question 7

Limited Table M / Table L

Expected Loss Cost

Answer 7

Limited Table M: k*E[A] + charge(r) * E[Ad]

Table L: charge(r) * E[A]

Question 8

Limited Table M / Table L

Basic Limit Premium

Answer 8

B(LM) = e-(c-1)E[A]+c(I+kE[A])
B(L) = e-(c-1)E[A]+cI
* Same as regular table M

Question 9

Large Dollar Deductible (LDD) Pricing

LDD Premium

Answer 9

Numerator: ELoss Cost + EA + Fixed Expenses
Denominator: 1-varies by premium

Question 10

ICRLL Approx

Adjusted Expected Loss

Answer 10

AEL = E[A] * State Hazard Group Diff * (1+0.8k) / (1-k)