Sahasrabuddhe

Question 1

2 requirements of claim size model

Answer 1

1. parameters can be adjusted for impact of inflation
2. LEV and unlimited means can be easily calculated

Question 2

general process of Sahasrabuddhe (to get adj data @ latest cost levels and BL)

Answer 2

1. create trend indices - CY and AY
2. calc trend adjusted unlimited means = claim size parameters at other cost levels

theta(i,j) = theta(n,j)*trend(i,j)/trend(n,j)

3. calculated trend adjusted limited means

LEV=theta(i,j)*(1-exp(-k/theta(i,j)) where k=limit

need to do this for raw triangle limit (PL) and BL

*for BL, only need latest row

4. calculate cumulative loss triangle adjusted to latest cost levels and basic limit

adj data(i,j) = raw data(i,j)*LEV(n,j) for BL/LEV(i,j) for PL

Question 3

Calculate development patterns by layer

Answer 3

Y is latest exposure period and BL

X is the layer you want

• calculate BL factors from adj cumulative data triangle and use these for Fy
• can now calc factors for any layer and any exposure period using the relationship
• if lower layer is not 0, use subtraction to get LEV for X

LEV for layer from 500K to 1M = LEV@1M-LEV@500K

Question 4

why is using sahasrabuddhe an improvement over standard CL?

Answer 4

-if use std chain ladder LDF, understate reserves

***improvement over applying standard CL to raw unadjusted data because it demonstrates that development factors at different cost levels and different layers are related to each other based on claim size models and trends

Question 5

if only calculating CDFs for BL

Answer 5

need LEVs @ PL for the normal triangle

Question 6

if calculating LDFs for other layers

Answer 6

need LEVs @ PL for square not just triangle

Question 7

if claim size models are only available at ultimate and latest cost levels -> simplified model formula

formulas for Fy, U, R

Answer 7

U=LEV Xin/LEV Yin = ratio at ultimate

R=LEV Xij/LEV Yij = selected ratio

Question 8

what does decay factor insure

Answer 8

R is high at early maturities and low at later -> R should be closer to 0 @ later maturities since more losses will be capped if X is lower limit

Question 9

observed ratio

Answer 9

actual losses limited by PL/actual losses limited by BL

@ same maturity

Question 10

for simplified model formula, may be easiest to make table

Answer 10

maturity, trended unlimited mean @ ultimate, LEV @ BL @ ult, LEV @ PL @ ult, ratio @ ult, decay factor, selected ratio

Question 11

for simplified model formula where layer does not have lower limit of 0

Answer 11

Fx=Fy*(1-U)/(1-R)

where U and R are calculated if lower limit was 0

Question 12

key benefit of simplified model formula

Answer 12

do not need to know claim size distribution @ earlier development period

only use claim size model at ultimate to calculate ultimate ratio and then estimate some selected ratios for some earlier development periods