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Transcript of 2008 Orlando Annual 20
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SOA 08 Annual Meeting & Exhibit
October 19-22, 2008
Session 20, Disability Modeling—Designing Effective
and Efficient Models
Moderator
Scott D. Haglund, FSA, MAAA
Authors
Lijia Guo, ASA, MAAA
Trevor C. Howes, FSA, FCIA, MAAA
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Lijia Guo, Ph.D., ASA, MAAA
Society of
Actuaries
2008 Annual Meeting, Session 20
October 20, 2008
0Lijia Guo SOA 2008 Annual Meeting
Agenda
IntroductionIntroduction
Generalized Linear Models
Data Mining (DM)
Fully Stochastic Models & Risks Integration
Summary
Lijia Guo SOA 2008 Annual Meeting 1
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Why Stochastic
Modeling
Pricing & Underwriting Produce a full distribution of possible outcomes
Confidence levels of held reserves
Consider the volatility of the unpaid claims Individual lines Correlation across the various lines
VAR, CTE
Regulatory and compliance Solvency II IFRS / Fair value accounting Public companies (SEC)
ERM Financial and capital management Operational/strategic excellence
Lijia Guo SOA 2008 Annual Meeting 2
Stochastic Modeling
Generalized Linear Models (GLM)
Generalized Additive Models (GAM)
Data Mining (DM)
Fully Stochastic Models (FSM)
Contingent claim Model (Stochastic Process)
Other Statistics Methods
3Lijia Guo SOA 2008 Annual Meeting
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Agenda
Introduction
Generalized Linear ModelsGeneralized Linear Models
Data Mining (DM)
Fully Stochastic Models & Risks Integration
Summary
Lijia Guo SOA 2008 Annual Meeting 4
Stochastic Models
‐ GLM
iμ
iii
i
j
j jiii
V Y Var
X gY E
ω μ φ
ξ β μ
/)(][
)(][ ,
1
=
+== ∑−
•For each observation i , from distribution with mean
•Y
has
distribution
from
the
exponential
family•g – is called the link function
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Stochastic Models ‐ GLM
Y
1
The identity link: g(Y) = Y
The log link: g(Y) = ln(Y)
The inverse link: g(Y) =
The logit link: g(Y) = )1
ln(Y
Y
−
Stochastic Models
‐ GLM
22
22
)(,)(,
)(,)(,1
)(,1)(,
μ φ
μ φ
σ σ φ
k Y Var x xV k
Y Var x xV
Y Var xV
===
===
===
iii V Y Var ω φ /)(][ =
For Normal:
For Poisson:
For
Gamma:
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Stochastic Models ‐ GLM
⎟ ⎠
⎞⎜⎝
⎛
− x
x
1ln
φ
2 x
ω
ξ
Y Claim
Frequency Claim #
Average
Claim
Amount
Prob./Lapse
g lnx lnx lnx
Error Poisson Poisson Gamma Binomial
1 1 Estimated 1
V(x) x x x(1‐x)
Exposure 1 # claims 1
0 ln(exposure) 0 0
Stochastic Models
– GLM
Applications
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Stochastic Models – GLM Applications
What to do with continuous variables? – Age, Claim Size…
Stochastic Models
‐ GAM
•GLMs are special case of GAMs
•Example
LN(E[PP]) = + f1(age) + f2(gender) +f3(Income) +f4(marital)
•The functions f1,f2,f3,f4 can be anything
‐GLM ‐ Categorical, polynomial, transforms
‐Non‐parametric functional smoothers
‐
Decision
trees
•Balance degrees of freedom, amount of data, and
functional form better
11Lijia Guo SOA 2008 Annual Meeting
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Stochastic Models ‐ GAM
• Error Criteria
∑ {Yi – g(ti) } ² + λ ∫ { g” (t)} ² dt
‐ λ is smoothing parameter
• Applications – P&C
• Reference:
‐ Nonparametric Regression and Generalized Linear Models, Green& Silverman
12Lijia Guo SOA 2008 Annual Meeting
Agenda
Introduction
Generalized Linear Models
Data MiningData Mining
Fully Stochastic Models & Risks Integration
Summary
Lijia Guo SOA 2008 Annual Meeting 13
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Lijia Guo SOA 2008 Annual Meeting 14
Stochastic Models
– Data
Mining
An information discovery process.
Knowing your goals Identifying responsive potential customers
Identifying existing customers that more likely to terminate
Identifying low risk purchaser
Identifying the factors that cause large claims
Indentifying interactions among risk factors
Choosing the right methods
Understanding the
limitations
Validation and testing
Make crucial business decisions
Lijia Guo SOA 2008 Annual Meeting 15
Data Mining ‐ Data
Identifying Data
Internal Sources Demographic data
Transactional data
Survey data
External Sources Databases
Survey Data
Competitor
Preparing Data
Transforming Data
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Lijia Guo SOA 2008 Annual Meeting 16
Introduction – DM Process
Stochastic Models
– Data
Mining
Decision Trees
Logistic regression
Neural Networks
Fuzzy Logics
Genetic Algorithms
Clustering
Associated discovery
Sequence Discovery
Bayesian analysis
Visualization
Hybrid
Algorithms
• Problems with standard algorithms
• Advanced algorithms
• Discovery-driven approaches
• Mixture of algorithms
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Lijia Guo SOA 2008 Annual Meeting 18
What is the best method for you?
Model Assessment
Goodness‐of ‐ fit
Prediction accuracy
Sensitivity and Specificity
ROC curve
Model diagnostics
Pearson Residuals
Deviance Residuals
Hat
Matrix
Diagonal
Lijia Guo SOA 2008 Annual Meeting 19
Model Validation
Cross validation
Avoid misleading
Improve the accuracy
Bootstrap validation
More robust solutions
Confidence measure
Sliding Window validation – for time‐series data
Non‐stationary
Slow‐varying
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20
DM in Variable Selection
Improving model accuracy and efficiency
Reducing model complexity/over fitting
Problem
‐‐ Given {Y,X} where
Find F, such that
Find and F*, such that, Z X ⊂( )F X Y ≈
*( )F X Y ≈
1 2{ , ,... } N
X x x x=
Lijia Guo SOA 2008 Annual Meeting 21
Case Study ‐ DM in Underwriting
Data: Group Health with over 100 input variables
Goal: Practical guide for underwriters to use for rates
adjustments
Principle Components Analysis applied
Regression Tree
Final model uses about 10% of the original variables
Improved
profitability
by
50%
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Lijia Guo SOA 2008 Annual Meeting 22
Regression Tree Example
Profit=6.5%+0.8% , if AS > 421
-0.5% , otherwise
+1.2% , if maleyoung than 30
-1.1% , otherwise
Two Predictor Dependence For
PROFIT_MARGIN
-0.10
-0.05
0.00
0.05
5000 10000 15000 20000 25000
P a r t i a l D e p e n d e n c e
AVG_SALARY
Two V ariable Dependen ce f or PROFIT_MARGIN; Slice SIZE = 0.99999999
PROFIT_MARGIN
-0.05
0.00
0.05
5000 10000 15000 20000 25000
P a r t i a l D e p e n d e n c e
AVG_SALA RY
Two Variable Dependence for PROFIT_MARGIN; Slice SIZE = 1.02702701
PROFIT_MARGIN
Lijia Guo SOA 2008 Annual Meeting 23
Case Study
‐ Stats
and
Variable
Importance
Input Additive Multiplicative Importance
Variable 1 0.2679 0.2690 100.00
Variable 2 0.2779 0.3203 75.23
Variable 3 0.1456 0.1771 54.65
…
Variable 9 0.1129 0.1148 23.37
Pair Variables Additive Multiplicative
Variable 1 & Variable 2 0.3714 0.3847
Variable 2 & Variable 3 0.3704 0.4066
…
Variable 4 & Variable 7 0.2417 0.2592
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Desirable Features of a Data Mining
Method Any nonlinear relationship can be approximated
A method that works when the form of the nonlinearity is
unknown
The effect of interactions can be easily determined and
incorporated into the model
The method generalizes well on out‐of sample data
24Lijia Guo SOA 2008 Annual Meeting
DM Applications in Insurance
Underwriting
Pricing/Rate Making
Claim Scoring
Risk Management
Policy Level Analysis
Cluster Analysis
Variable Selection
Effect
of
Plan
design
on
utilization
and
distributions
Trends and Projections
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Agenda
Introduction
Generalized Linear Models
Data Mining
Fully Stochastic Models & Risks IntegrationFully Stochastic Models & Risks Integration
Summary
Lijia Guo SOA 2008 Annual Meeting 26
Fully Stochastic Model (FSM)
Risk Scenarios
Economic scenarios
Underwriting risk scenarios
Policyholder behavior
Integrating Risks and Correlations
At Product
level
At Enterprise level
Model Efficiency and Applications
27Lijia Guo SOA 2008 Annual Meeting
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Scenarios
scenario simulation
historical filtered historical Monte Carlo
simulation simulation simulation
volatility correlation
scaling scaling
EWMA GARCH
28Lijia Guo SOA 2008 Annual Meeting
Case Study
‐ Insurance
Package
Age of insured: 60
Unreduced death benefit 500,000
Deferred annuity
Monthly LTC benefit: min(10,000I(t), %AV), where
I(t) – indexed to the inflation
%AV varies depending on the states of care (ADLs)
Death benefit for disabled: %AV
Maximum LTC benefit: 200,000
Waiting period:
2 years
29Lijia Guo SOA 2008 Annual Meeting
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Stochastic Modeling Insurance
Package
Risk Measure in
Credit Risk
Market Risk
Insurance RiskInsurance Risk
Contingency risks
Catastrophe (Influenza
Pandemic)
Business continuity
Claims
Liquidity
Reinsurance
Risk based value Pricing Underwriting
Reserving
Mortality Risk
General population
Disabled lives
Morbidity Risk
Lapse
Interest risks
Underwriting (anti selection)
Embedded Options
Risks Interaction/correlation Claim reserve
30Lijia Guo SOA 2008 Annual Meeting
Modeling Insurance Package
‐ contract premium payable at BOY
‐ Discount function
n ‐ Term/length of the contract
APV of the policy premium is
Note the correlations of risks
)()()()()(Pr LTCB APV WB APV DA APV DB APV emiums APV +++=
T v
k P
)'1)('1)('1())(Pr( )()()()( i
xk
w
xk
d
xk xk qqqt xT p −−−=>=τ
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LTC Combo ‐ Stochastic Interest Rate
The discount
factor
for
the
cash
flows
at
the
EOY
t is
Where
is the interest rate prevailing in year t:
Example
)1()1)(1(
1
21 t
t r r r
v+++
=L
t r
dzdt r mqdr t t σ +−= )(
004.,0601.,015. === σ mq
LTC Combo ‐ Stochastic Lapse Rate
The lapse rate in year t is
Where
is US 1‐ year T‐bill rate in year t.
Example.
22.,82. 21 == β β
t r
)1,0(,12
)(
11
)( N r qq t t t
w
t
w
t ≈++= −− ε ε β β
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LTC Combo ‐ Stochastic Mortality Rate
Mortality Risk: Uncertainty
in
future
mortality
rates
including
increases
and
decreases in mortality rates
Lee‐Carter Model
Cairns‐Blake‐Dowd Model
Longevity Risk: Uncertainty in the long‐term trend in mortality rates.
Normally taken to mean the risk that survival rates are higher than
anticipated.
Short ‐Term, Catastrophic Risk: Risk that over short periods of time, mortality
rates are much higher (or lower) than would normally be experienced. (e.g.,
influenza
pandemic
of
1918).
Stochastic Morbidity Models
‐ LTC benefit paid at different state j of disability, j =1, 2, 3.
‐ Transition probability from State i at time z to State j at time t:
),(
1
ji
k b +
( )∑ ∑=
+
=+ +++=
n
k
xk
k
j
ji
ji
k pvk xk xPb LTCB APV 1
)(13
1
,
),(
1 )1,()( τ
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Stochastic Morbidity Models
is the
force
of
transition
from
state
i to
State
j at
time t.
State Transitions in LTC insurance – state of care:
)(, t jiλ
Risk Scenarios
scenario simulation
historical filtered historical Monte Carlo
simulation simulation simulation
volatility correlation
scaling scaling
EWMA GARCH
Monte Carlo (single and multi‐step)
Historical
Stress scenarios, sensitivity shocks
Additive and multiplicative shocks to any risk factor or risk factor node
Principle component analysis, factor reduction, risk‐factor clustering
37Lijia Guo SOA 2008 Annual Meeting
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Scenario s
Interest Rate
Spread
Mortality
MobidityTotal EC
• Multiple individual scenario sets by risk types• Asset and liabilities cash flows are modeled with the 4 scenario sets
• EC calculated based on individual distribution
• Total EC calculated based on the aggregation
38Lijia Guo SOA 2008 Annual Meeting
Integrating Product Risk/Return
39
0
5
10
15
20
25
Yr 1 2 3 4 5 6
0
5
10
15
20
25
30
35
Yr 1 2 3 4 5 6 7
0
5
10
15
20
25
Yr 1 2 3 4 5 6
-10
-5
0
5
10
15
20
25
30
Yr 1 2 3 4 5 6 7
Time
Enterprise Economic Profit
Product 1 Product 2 Product 3 Product 4
Lijia Guo SOA 2008 Annual Meeting
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Effect of Risk Aggregation
40Lijia Guo SOA 2008 Annual Meeting
Summary Stochastic Modeling provides insight into both A&L
uncertainty
Stochastic models are more complex than traditional models but this makes actuarial analysis and judgment even more
important
Regulatory focus on risk management and disclosure is increasing demand
Optimal Risk Adjusted Return ‐ increase enterprise economic
profit
Q&A
41Lijia Guo SOA 2008 Annual Meeting
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References
England, P and Verrall, R (1999). “Analytic and Bootstrap Estimates
of Prediction Errors in Claims Reserving,” Insurance: Mathematics
and Economics
Guo, L (2001). “Dynamic Method for the Valuation of Fair Value
Insurance Liabilities”, Casualty Actuarial Society, www.casact.org
Guo, L (2003), “ Applying Data Mining Techniques in
Property/Casualty Insurance”, Casualty Actuarial Society ,
www.casact.org
Guo, L (2003), “Data Mining in Insurance Seminar”, Society of
Actuaries, www.soa.org
Guo, L (2007), “Stochastic Modeling in Health Benefits”, Society of
Actuaries, www.soa.org
42Lijia Guo SOA 2008 Annual Meeting
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Disability Modeling:Designing Effective and
Efficient Models
Trevor Howes, FCIA, FSA, MAAA
SOA Annual Meeting – OrlandoSession 20
October 20, 2008
Session 20 PD - Trevor Howes 2
Agenda
• Modeling demands
• Model Efficiency Work Group
• Mathematical and modeltechniques
• Hardware Technology
• Software Technology
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Session 20 PD - Trevor Howes 3
Pending Issues ImpactingDisability Models
• Principle-based Approach to reservesand RBC capital – Robust, seriatim deterministic reserve
using gross premium method
– Unlocked assumptions appropriate tobusiness and driven by experience
– Stochastic Reserves and Capital
– Single model for both purposes ?
Session 20 PD - Trevor Howes 4
Pending Issues ImpactingDisability Models
• IFRS (Europe, Canada, Asia, SEC, US?)
• ERM and Economic Capital(Management, Ratings agencies,Parent Corporations)
• Capital Assessment (Solvency II,proposed Canadian MCCSR)
• NAIC has adopted a SolvencyModernization Work Plan (June, 2008)
• Will NAIC adopt IFRS before PBA?
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Session 20 PD - Trevor Howes 5
Common threads
• Realistic, probabilistic, risk based focus
• Blend of deterministic and stochastic
• 1000’s or 10’s of 1000’s of scenarios
• Risk of higher volatility of results
• Need for reliability and robustness
• Increased scrutiny of actuary’s judgment and quality of models
Session 20 PD - Trevor Howes 6
Implications on Modeling
• Models must become more effective,more efficient AND … – More granular and policy/plan specific
– More precise for all material risks
– More adaptable to multiple purposes
– More flexible to respond to changes
– More easily documented and audited
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Session 20 PD - Trevor Howes 7
Implications on Modeling
• Actuaries must become more effectiveand efficient at modeling
– Need more time for interpretationand analysis of model results
– Spend less time
• building business models
• entering and verifying assumptions
• testing and validating• documenting
Session 20 PD - Trevor Howes 8
Model Efficiency Work Group
• MEWG is a subgroup of the AAA SVL2Committee created in 2007
• Mandate to examine ways to make thecomplex modeling required under PBAmore manageable
• Techniques being examined could
apply generally to all modelingincluding disability
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Session 20 PD - Trevor Howes 9
Modeling EfficiencyBibliography
• Actuarial Modeling Techniques
– Scenario design and selection
– Mathematical or model design
– Model data building
• Technology Solutions
– Hardware design
– Software design
• Website link:http://www.actuary.org/risk/pdf/bibliography.pdf
Session 20 PD - Trevor Howes 10
Modeling EfficiencyFor Disability
• Scenario design and selection – stochastic analysis of economic risks
– e.g. PBA and Economic Capital
• Are these relevant or practical forDisability models? – DI has long term interest rate risks
– ALM analysis is useful
– Useful to link dynamic policyholderbehavior to economic scenarios
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Session 20 PD - Trevor Howes 11
Modeling EfficiencyFor Disability
• Scenario testing requires detailedmodels reflecting realistic cash flows
• Full multi-state model vs. claims costs
– Economic risks impacted by claim runoff
– Termination rates may vary by scenario
– Required to properly understand thebusiness
• Magnifies need for model efficiency
Session 20 PD - Trevor Howes 12
Modeling EfficiencyFor Disability
• Mathematical or model design
– Closed form solutions to optionpricing
– Low discrepancy sequences (Quasi-Monte Carlo) vs. full Monte Carlo
– Replicating portfolios
– Predictive models
– Low relevance to Disability models
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Session 20 PD - Trevor Howes 13
Modeling EfficiencyFor Disability
• Model data building techniques
– Most common solution to runtimeand technology constraints
– Build compressed model using
• Grouped data at selected model points
• Representative plans and risk classes
–
Critical area for Disability models dueto runtimes and data heterogeneity
Session 20 PD - Trevor Howes 14
Modeling EfficiencyFor Disability
• Drawbacks of compressing in forcedisability insurance data – Low compression ratios
– Result distortion (model error)
• Especially if risk class substitution
– High effort to create and validate
– Complicates multiple uses of model
• Preferable to use full seriatim ordynamic option to build and selectcompressed version as needed
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Session 20 PD - Trevor Howes 15
Modeling EfficiencyFor Disability
• Building compressed models – New techniques (Cluster Analysis)
– Adjust compression ratio by blockaccording to sensitivity/significance
– Calibrate and test according to purpose
– Generate both full seriatim andcompressed models for comparison testing,validation, adjusting compression
– Automate compression if possible as partof data extract load & transformation
Session 20 PD - Trevor Howes 16
Technology –hardware solutions?
• For Stochastic analysis, may needfurther 100 to 1000X improvementwhile also meeting requirements for
– Reasonable total cost (hardware, software,IT infrastructure and support)
– Increased reliability, auditability, control
– Increased actuarial productivity and value
• Will technology enable efficientdisability models in foreseeable future?
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Session 20 PD - Trevor Howes 17
Technology performance review
• Technology has delivered incrediblyconsistent performance improvements
• For example, over past 10 years, youcould purchase desktop PCs based on:
– 1998 (Pentium II, 400 MHz)
– 2003 (Pentium 4, 2.53 GHz)
– 2008 (Core 2 Quad, 2.66 GHz)
Session 20 PD - Trevor Howes 18
PC Performance1998 - 2008
59.2.017Core2 Quad
2.66GHz
2008
5.8.172Pent 42.53GHz
2003
1.01.000Pent II400MHz
1998
BenchmarkSpeed
BenchmarkTime
Processor Year
Estimates based on seriatim actuarial projection model
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Session 20 PD - Trevor Howes 19
PC Performance per $11998 - 2008
133.2$2000Core2 Quad2.66GHz
2008
12.5$2100Pent 42.53GHz
2003
1.0$4500Pent II400MHz
1998
Benchmark Value
ApproxCost
Processor Year
Session 20 PD - Trevor Howes 20
Historical TechnologyImprovements
• Miniaturization has enabled
– higher transistor counts
– faster response
– increased clock speeds
– more instructions per second
– faster buses
• Reduced voltages to manage heat
• Faster and denser memory and drives
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Session 20 PD - Trevor Howes 21
Future Innovations
• New materials (hafnium oxide)
• Deep UV optical lithography
• Nanotechnology (molecular level)
• Helium supercooled transistors
• Terahertz transistor
• Trigate transistors (3-d)
• Biocomputing & neural networks
• Quantum computing
Session 20 PD - Trevor Howes 22
Current Technology Trends
• Increased parallelism in processors
– Multiple instructions executed at once
• Multiple processor cores on one chip
– Faster than multiprocessors
– Shorter distances
– Shared bus and cache
– Interface at higher clock speeds
• Intel plans chips with 100+ cores
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Session 20 PD - Trevor Howes 23
Personal Grids?
• Personal Cluster “deskside” server
– 340 Gigaflops of computing power
– 8 quad-core processors (32 cores)
– 1 Terabyte disk storage
– Regular 120V wall plug
– Windows CCS O/S installed
– Cost: under $20,000
Session 20 PD - Trevor Howes 24
Parallelism
• Parallelism requires multithreading
• Automatic benefit from OS tasks
• However significant benefit requiresspecific application design changes
– Identify separable non-linear tasks
– Manage thread synchronization
– Data sharing and management
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Session 20 PD - Trevor Howes 25
Parallelism and DistributedProcessing
• Distributed Processing requires
– Allocating processing steps to helpers
– Distributing work by Cells, seriatim policies,testing targets (scenarios)
– Monitoring task completion or failure
– Consolidation of results from helpers
– Specific application support
Session 20 PD - Trevor Howes 26
Parallelism and Grids
• In “Grid Computing” as typically used
– Focus on capturing spare capacity formany applications over large network
– Enterprise Grid Managers are notapplication specific or knowledgeable
– May require inserting additional code
– Software license and IT support per node
– 1000+ processors may achieve runtimesbut costly, inefficient, unreliable
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Session 20 PD - Trevor Howes 27
The Evolution of Grids
• Trend now to greater use of dedicatedserver farms and/or computer clusters
– Tightly coupled for efficiency
– Easy software installation
– Cost effective O/S and IT support
• Microsoft CCS 2003 & HPC Server 2008 enablessharing grid and scheduling
– Robust and audit friendly – Highly scalable to large farms
Session 20 PD - Trevor Howes 28
Technology Solution –Hardware?
• Will technology enable efficient but complexdisability models in foreseeable future? – Not enough for large stochastic applications yet
– Quite enough now for seriatim, first principles,multi-state models, selected scenarios
• Model efficiency must also consider humancosts of maintenance, control and analysis
• One actuary’s salary plus overhead = cost offarm of 250 + cores?
• Technology can make actuary moreproductive depending on application software
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Session 20 PD - Trevor Howes 29
Technology Solution –Software
• Detailed, first principles, multi-statemodel
– Optional claims cost approach
– Enable selective adjustment of eachcomponent of claims cost andunderstanding impact
– Support compound assumptions
– Facilitates experience analysis
Session 20 PD - Trevor Howes 30
Technology Solution –Software
• Full seriatim business model for bothvaluation and projection
– Optional selective compression
– Avoid reconciliation and validation
– Enable targeted adjustment of
assumptions at granular level – Supports experience analysis, source
of earnings, reserve movement
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Session 20 PD - Trevor Howes 31
Technology Solution –Software
• Multiple purpose, multiple basisprojection capabilities
– Avoid reconciliation and validation
– Ease of testing “what if” scenarios,reporting impact of changes
– Both deterministic and stochastic(?)
– Staff productivity with one platformto learn and maintain
Session 20 PD - Trevor Howes 32
Technology Solution –Software
• Store assumptions in objects separatefrom model framework, logic and code
– Promote control of code changes,stability, ease of validation, audit
– Facilitate assumption query,documentation, change
– Balance of control vs. flexibility
– Separation of duties; use of skills
7/23/2019 2008 Orlando Annual 20
http://slidepdf.com/reader/full/2008-orlando-annual-20 40/40
Session 20 PD - Trevor Howes 33
Technology Solution –Software
• Integrated automated model building – Load of source data and transformation to
feed model (avoid relying on IT dep’t)
– Compress? (if necessary)
– Define and apply rules
• to assign business to “supercells”
• to attach/update assumptions insupercells or at seriatim level
(to reduce numbers of supercells) – Enable auditable start to end batch process
Session 20 PD - Trevor Howes 34
Efficient andEffective Models
• Avoid over simplification of models
– Seriatim, first principles, flexible
• MEWG is studying model efficiencytechniques
• Hardware technology will help
• Software design is critical to userproductivity with models