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Using Simulation Modeling to
Evaluate a Medical Insurer's
Reinsurance Coverage
A Case Study
By Lina S. Chan, FSA, MAAA, FCA
Domingo Castelo Joaquin, Illinois State University
© 2011 by Lina S. Chan and Domingo Castelo Joaquin
1
Something about
Lina S. Chan, FSA, MAAA, FCA
Domingo Castelo Joaquin
Using Simulation Modeling to Evaluate a
Medical Insurer's Reinsurance Coverage
–A Case Study
2
Lina S. Chan, FSA, MAAA, FCA, is the managing
partner and founder of CP Risk Solutions, LLC. CP is a
consulting firm providing actuarial, underwriting and
related risk management services to insurers,
reinsurers, investors, third party administrators,
managing general underwriters/agents, benefit
management companies, and other risk assuming
companies.
lina@cprisksolutions.com
3
Using Simulation Modeling to
Evaluate a Medical Insurer's
Reinsurance Coverage - A Case Study
Domingo Castelo Joaquin, Professor Illinois State University
Domingo Castelo Joaquin is Associate Professor of Finance at
Illinois State University. He specializes in decision theory,
financial modeling, and real options valuation. His works have
appeared in the Journal of Post Keynesian Economics, Theory &
Decision, Economic Letters, Quarterly Review of Economics and
Finance, Risk Management and Insurance Review, and the
Journal of International Money and Finance. His work has been
cited in CNNfn, the New York Times, Money Magazine,
Kiplinger’s, Time.com and other publications. He received his
Ph.D. in Business Administration from Michigan State University
(1997).
dcjoaqu@ilstu.edu
4
The Case
A small insurance company evaluating request for
proposal to provide stop-loss coverage
• The policy covers the group up to $800,000 per individual after
the group pays for the first $200,000 for each individual
• Huge risk exposure relative to the insurer’s capital size.
N=20,000 exposures.
• The insurance company wants the business but also wants to
preserve its capital ($15,000,000) so it does not get into the
Insurance Department's watch list.
5
Using simulation modeling to support a
medical insurer’s reinsurance decision
• Output variable: Ending Capital Position
• Input variables: Claims frequency and individual loss
severity
• Decision variables: Alternative reinsurance options for the
stop-loss provider.
• Sensitivity analysis: Alternative claims distributions
6
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# of Indivduals
Individual Claim Distribution
17,853
93
80
60
40
27
13
1
3
-
7
200,000
12.00
150,000
9.00
100,000
6.00
50,000
3.00
-
Untrended Excess
Claim Frequncy Per
10,000 Exposure
Average Untrended
Excess Claim Severity
Historical Un-trended Excess Claims
2000
2001
2002
2003
2004
2005
Incidence Year
Average Untrended Excess Claim Severity
Untrended Excess Claim Frequency per 10,000
8
Trended PPPM Excess Claims
Year
Annual
Trend
Cumulative
Trend Factor to
2005
2000
2001
2002
2003
2004
2005
11%
12%
13%
13%
12%
1.78
1.60
1.43
1.27
1.12
1.00
9
Simulating the Stop Loss Opportunity
• Opportunity is profitable on “Average”
• What is the variability around this average?
• What is the probability that the capital position would improve?
• What is the probability that the capital position would be depleted?
10
Base Case Ending Capital Position
•
•
•
•
•
•
EC = Ending capital = S + NI
S = Starting Capital = $15,000,000
NI = Net Income After Tax = NIBT x (1 – T%)
NIBT = Net Income Before Tax = P – C - A
T% = Assumed Tax Rate = 35%
P = Premium Revenue = $3,240,000 = $13.50 PPPM x 12 Months x
20,000 Exposures
• C = Stop loss claims = Simulated stop loss claims
• A = Administrative expenses = $278,200 = $100,000 + 5.5% x P
11
Fitted Claim Frequency Distribution
• Poisson distribution
•
•
•
•
•
•
Assume loss events are independent
n=20,000 exposure
P=1.10%
Average: np = 220.99
Variance: np(1-p) = 218.55
Average ~ Variance
Incidence year
Frequency
Exposure
Relative
Frequency
2000
2001
2002
2003
2004
2005
Total/Composite
96
142
123
225
159
150
895
10,000
11,000
12,000
14,000
16,000
18,000
81,000
0.009600
0.012909
0.010250
0.016071
0.009938
0.008333
0.011049
12
Fitted Loss Frequency
and Loss Severity
Distributions
• Poisson distribution to model claims frequency
• Generalized beta distribution to model severity of claims from known
sources
• Generalized beta distribution to model the distribution of 2006 trend
factors.
• Three best fitting distributions for trended claims (out of more than
ten continuous parametric distributions with positive support. )
Model 1:
Lognormal
Model 2:
Inverse Gauss
Model 3:
Log Logistic
13
Base Case Simulation Results
(1)
Minimum
Maximum
Mean
Standard Deviation
Variance
Skewness
Kurtosis
Number of Errors
Mode
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
50.0%
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
Pr(End Cap > Start Cap)
Pr(Lose at least 5%)
(2)
(3)
(4)
Model 1
Model 2
Model 3
13,016,180
16,308,390
15,096,990
476,066
226,638,700,000
(0.54)
3.33
15,261,760
13,239,700
16,330,050
15,200,800
411,814
169,590,500,000
(0.50)
3.42
15,359,460
10,684,770
16,197,110
14,384,980
696,552
485,184,300,000
(0.43)
3.21
14,246,240
14,236,050
14,457,140
14,607,680
14,707,870
14,803,430
14,886,180
14,956,940
15,019,420
15,083,460
15,141,330
15,196,480
15,256,880
15,316,120
15,377,970
15,436,370
15,507,210
15,581,310
15,673,920
15,794,830
61.6%
5.2%
14,468,640
14,657,730
14,777,410
14,864,240
14,949,700
15,017,570
15,072,650
15,126,920
15,181,040
15,235,360
15,284,080
15,334,450
15,385,610
15,441,650
15,491,520
15,549,600
15,616,050
15,697,850
15,821,650
71.4%
1.9%
13,160,680
13,450,260
13,663,460
13,821,670
13,953,090
14,056,990
14,163,760
14,253,170
14,348,060
14,435,680
14,526,420
14,609,330
14,691,060
14,780,080
14,880,000
14,984,700
15,093,710
15,242,110
15,450,260
19.4%
39.8%
14
Managing downside risk with Reinsurance
• What is reinsurance?
• Why use reinsurance?
• Who uses reinsurance?
• What are the reinsurance structure?
15
Reinsurance Structures
•
Excess of Loss – Specific and/or Aggregate
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Reinsurance Structures
•
Quota Share
Simple Arithmetic Example
– 50% quota share, 20% ceding commission (administrative allowance)
Insurer’s
Retention
Reinsurer’s
Assumption
Total
$5 MM
$5 MM
$10 MM
Ceding Commission
+ $1 MM
- $1 MM
$0 MM
Claims
- $4 MM
- $4 MM
- $8 MM
$2 MM
$0 MM
$2 MM
Premium
Net Income before actual administrative expenses & tax
17
Managing downside risk with Reinsurance
The Case Study - Two alternative risk management strategies:
(1) a 50% quota share reinsurance
(2) an aggregate excess reinsurance combined with a 50% quota
share reinsurance.
18
Capital position
with 50% quota share reinsurance
•
•
•
•
•
•
•
•
•
•
•
•
NIBT = Net Income Before Tax
= P – C – A – (RP–RC–CC) = (P–RP) – (C-RC) – (A-CC)
P = Premium revenue = $3,240,000
C = Stop loss claims = Simulated stop loss claims
A = Administrative expenses = $278,200
RP = Ceded quota share reinsurance premium revenue = 50% x P = $1,620,000
CC = Quota share reinsurance ceding commission = 10% x RP = $162,000
RC = Quota share reinsurance claim recovery = 50% x Stop loss claim.
19
Capital position
20
Capital position
(1)
Minimum
Maximum
Mean
Standard Deviation
Variance
Skewness
Kurtosis
Number of Errors
Mode
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
50.0%
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
(2)
Model 1
(3)
Model 2
(4)
Model 3
14,022,970
15,669,080
15,063,380
238,033
56,659,680,000
(0.54)
3.33
15,145,760
14,134,740
15,679,910
15,115,280
205,907
42,397,630,000
(0.50)
3.42
15,194,610
12,857,270
15,613,440
14,707,380
348,276
121,296,100,000
(0.43)
3.21
14,638,000
14,632,910
14,743,460
14,818,720
14,868,820
14,916,600
14,957,970
14,993,360
15,024,600
15,056,620
15,085,550
15,113,130
15,143,320
15,172,950
15,203,870
15,233,070
15,268,490
15,305,540
15,351,840
15,412,300
14,749,210
14,843,750
14,903,590
14,947,000
14,989,740
15,023,670
15,051,210
15,078,350
15,105,400
15,132,560
15,156,930
15,182,110
15,207,690
15,235,710
15,260,640
15,289,690
15,322,910
15,363,810
15,425,710
14,095,220
14,240,020
14,346,610
14,425,720
14,491,430
14,543,380
14,596,760
14,641,470
14,688,910
14,732,720
14,778,100
14,819,550
14,860,410
14,904,930
14,954,890
15,007,240
15,061,740
15,135,940
15,240,020
64.0%
1.1%
73.6%
0.1%
20.6%
10.4%
21
Capital position
with 50% quota share reinsurance + aggregate excess
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
NIBT = Net Income Before Tax = (P–C–A)–(RP–RC–CC)–(ARP–ARC)
=(P – RP - ARP) - (C – CC - ARC) - (A - CC)
P = Premium revenue = $3,240,000
C = Stop loss claims = Simulated stop loss claims
A = Administrative expenses = $278,200
RP = Ceded quota share reinsurance premium revenue = 50% x P = $1,620,000
CC = Quota share reinsurance ceding commission = 10% x RP = $162,000
RC = Quota share reinsurance claim recovery = 50% x Stop loss clam
ARP = Aggregate excess reinsurance premium = $100,000
ARA = Aggregate excess attachment point = $1,950,000
ARM = Aggregate excess maximum coverage = $1,000,000
ARC = Aggregate excess reinsurance recovery
= MIN(MAX[(C – RC) – ARA,0],ARM)
22
Capital position
23
Capital position
(1)
Minimum
Maximum
Mean
Standard Deviation
Variance
Skewness
Kurtosis
Number of Errors
Mode
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
50.0%
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
(2)
Model 1
14,607,970
15,604,080
15,009,880
213,237
45,470,180,000
(0.04)
2.23
14,644,970
14,644,970
14,678,460
14,753,720
14,803,820
14,851,600
14,892,970
14,928,360
14,959,600
14,991,620
15,020,550
15,048,130
15,078,320
15,107,950
15,138,870
15,168,070
15,203,490
15,240,540
15,286,840
15,347,300
53.5%
0%
(3)
Model 2
14,644,970
15,614,910
15,054,320
195,532
38,232,680,000
(0.20)
2.52
14,644,970
(4)
Model 3
13,442,270
15,548,440
14,774,610
196,780
38,722,300,000
0.85
4.30
14,644,970
14,684,210
14,778,750
14,838,590
14,882,000
14,924,740
14,958,670
14,986,210
15,013,350
15,040,400
15,067,560
15,091,930
15,117,110
15,142,690
15,170,710
15,195,640
15,224,690
15,257,910
15,298,810
15,360,710
62.5%
0%
14,644,970
14,644,970
14,644,970
14,644,970
14,644,970
14,644,970
14,644,970
14,644,970
14,644,970
14,667,720
14,713,100
14,754,550
14,795,410
14,839,930
14,889,890
14,942,240
14,996,740
15,070,940
15,175,020
14.8%
0.5%
24
Sensitivity Analyses
Number of claims filed with
trust
Claim severity/3rd known
condition
Claim severity/4th known
condition
Claim severity/unknown
condition
2006 trend factor
Standardized Beta
/ Without
Reinsurance
Standardized
Beta / 50%
Quota Share
Standardized Beta / with
Aggregate Excess
(0.170)
(0.170)
(0.170)
(0.087)
(0.087)
(0.088)
(0.080)
(0.080)
(0.082)
(0.068) to
(0.082)
(0.068) to
(0.082)
(0.065) to (0.077)
(0.075)
(0.075)
(0.075)
25
Weakness in the contractual relationship: Medical insurer relies on the
self-funded, self-administered Trust to perform accurate and unbiased
administration consistent with guidelines.
Risk management procedures:
Clear administration and stop loss agreements with strong contractual
ramifications
Frequent underwriting, claim and transactional audits on the Trust’s
administration Monitoring such as on-going claim experience reports,
reports on individuals hitting catastrophic claim diagnosis, and reports on
individuals reaching 50% of deductible
Claims and medical management support such as health care provider
reimbursement negotiations, contracts with tertiary care and specialty
provider network networks
Close working relationship with the Trust as an “involved” partner
informed of underwriting and administration development
26
Critical Risk Management Issues
The model results for management decision are performed. Now what?
• Actual will deviate expected.
• Actual could be on either side of the curve
• For desirable financial outcome, involved risk partners must have AIR
• Accountability
• Information
• Resources
• AIR for this Case Study
27
Questions?
Domingo Castelo Joaquin
28

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