Transcript Reserving for Health Insurance

Reserving for Health or Property
Casualty Insurance
Methods of Computing Loss Reserves
Meeting-cum-Seminar on Preparedness towards De-tariffing Non-life Insurance
Hyderabad, March 13 & 14, 2006
Prepared by Thomas Kabele, FSA, BearingPoint
1
Need for Accurate Reserves
1. To compute accurate loss ratios claims should be on an
incurred basis.
2. Incurred = Paid Claims + Increase in Case Reserves +
Increase in IBNR.
3. Reserves are usually computed using Claim triangles.
Insurance Sector Reforms in India
INPUT – cumulative paid claims (lakh)
Accident
year
2003
2003 end
200
2004
2004 end
2005
2006
End
End
1010
1400
1400
250
1240
1750
300
1500
2005
2006
Total
350
200
1250
2950
5000
Insurance Sector Reforms in India
INPUT – Case Reserves
Accident
year
2003
2003 end
1100
2004
2004 end
2005
2006
end
end
350
0
0
1400
450
0
1700
550
2005
2006
Total
2000
1100
1750
2150
2550
Insurance Sector Reforms in India
Case Incurred =
Cum. Paid + Case Reserves
1300 = 200 + 1100; 1360 = 1010 + 350
Accident
year
2003
2003 end
1300
2004
2004 end
2005
2006
end
End
1360
1400
1400
1650
1690
1750
2000
2050
2005
2006
Total
2350
1300
3000
5090
7550
Insurance Sector Reforms in India
Projections Methods
1.
We can project “ultimate loss” using either cumulative paid
losses or using case incurred losses.
2.
The “reserve” is the ultimate loss less the “losses to date.” (i.e.
2006 end column)
3.
If the “losses to date” are “paid losses” then the “reserve” will
be the SUM of the Case and IBNR reserves.
4.
To compute the IBNR one must subtract the “case reserve”
from the SUM.
5.
To do the computations we show the triangles in the “actuary’s
format”
6.
LTD = Losses to Date = Losses for end of year 2006.
Insurance Sector Reforms in India
Paid Reserve Triangle in Actuary’s format
(i.e. shift rows to the left)
Accident
year
12 mo.
24 mo
36 mo
48 mo
2003
200
1010
1400
1400
2004
250
1240
1750
??
2005
300
1500
??
??
2006
350
??
??
??
2006
1100
4750
3150
1400
Insurance Sector Reforms in India
Link Ratios for Paid Data
5.0500 = 1010 / 200
AY
24/12
36/24
48/36
2003
5.0500
1.3861
1.0000
2004
4.9600
1.4113
2005
5.0000
Ave link
5.0033
1.3987
1.0000
Insurance Sector Reforms in India
Projected Values –
Paid Projection Method
5501.2 = 5.0033 * 1100; 7697.5 = 5501.2 * 1.3987
12 mo
24 mo
36 mo
48 mo
2003
200
1000
1400
1400
2004
250
1250
1750
1750.0
2005
300
1500
2098.1
2098.1
2006
350
1751.2
2449.4
2449.4
Total
1100
5501.2
7697.5
7697.5
Ave ratio
5.0033
1.3987
1.0000
Insurance Sector Reforms in India
IBNR and Ultimate Paid
Paid Projection Method
Accident year
Ultimate Paid
(48 mo)
LTD Paid
Loss to Date
Reserve
Total
Case
Reserve
IBNR
reserve
(1)
(2)
(3)= (1)-(2)
(4)
(5)=(3)-(4)
2003
1400
1400
0
0
0
2004
1750
1750
0
0
0
2005
2098.1
1500
598.1
550
48.1
2006
2449.4
350
2099.4
2000
99.4
Total
6297.5
3600
2697.5
2550
147.5
Insurance Sector Reforms in India
Actuary’s Format for Case Incurred
12 mo
24 mo
36 mo
48 mo
2003
1300
1360
1400
1400
2004
1650
1690
1750
??
2005
2000
2050
??
??
2006
2350
??
??
??
Total
7300
5100
3150
1400
Insurance Sector Reforms in India
Case Incurred Link Ratios
1.0462 = 1360/1300
24 / 12
36 / 24
48 / 36
2003
1.0462
1.0294
1.0000
2004
1.0242
1.0355
2005
1.0250
Ave link
1.0318
1.0325
1.0000
Insurance Sector Reforms in India
Projected Case Incurred
2424.7 = 1.0318 * 2350; 2503.4 = 1.0325 * 2424.7
12 mo
24 mo
36 mo
48 mo
203
1300
1360
1400
1400
2004
1650
1690
1750
1750.0
2005
2000
2050
2116.5
2116.5
2006
2350
2424.7
2503.4
2503.4
TOTAL
7300
7524.7
7770.0
7770.0
Ave link
1.0318
1.0325
1.0000
Insurance Sector Reforms in India
Ultimate and IBNR by case incurred
projection
Ultimate by Case
Incurred Projection
LTD case
incurred
IBNR case
incurred
IBNR paid
method
2003
1400
1400
0
0
2004
1750
1750
0
0
2005
2116.5
2050
66.5
48.1
2006
2503.4
2350
153.4
99.4
Total
7770.0
7550
220.0
147.5
Insurance Sector Reforms in India
“Age”
India uses fiscal year and fiscal year 2003-04 starts on 1st April
2003 and ends on 31st March 2004.
The triangles can be on a fiscal basis or calendar basis.
Claims that occur in 1st April 2003 are 12 months old on 31st
March 2004.
In the “actuary’s format” the “age” in the columns is the
maximum age.
Insurance Sector Reforms in India
Various Types of Policyholder Reserves (or
Provision)
1. Reserve for unexpired risk.
2. Mathematical Reserves (long term non cancelable
health, property, casualty contracts)
3. Loss Reserves (Case, IBNR)
4. Loss Adjustment Reserves (Defense, Adjusting)
5. Reserves (or Asset) for Audit and Retrospective
Premiums.
6. Reserves for “dividends” – also called bonuses and
experience refunds.
1, 3, 4 are most important
Insurance Sector Reforms in India
Total U.S. Reserves
as of 31st Dec. 1990 all property Casualty insurers
Reserve
Amount $ mil
Percent
1 Unexpired Risk
122,478
24.66%
2. Mathematical Reserve
included
--
3. Loss Reserves
303,1567
61.05
4. Loss Adjustment
65,146
13.12%
5. Audit Premiums
(3970)
0.80%
6. Bonuses, Dividends
1831
0.37%
Total
496,582
100.00%
Insurance Sector Reforms in India