Optimizing Multi-Period DFA Systems
Professor John M. Mulvey
Department of OR and Financial Engineering
Bendheim Center for Finance
Princeton University
July 2000
Strategic Asset and Liability Systems (DFA)
Towers Perrin-Tillinghast CAP:Link/OPT:Link, TAS significant impact (e.g. US West -- $450 to 1001 Million)
American/Munich Re-Insurance – ARMS Financial planning for individuals
– Home Account, Financial Engines KontraG bill in Germany
W. Ziemba and J. Mulvey, eds., World Wide Asset and Liability Modeling, Cambridge University Press, 1998
• Single models
Limitations of Traditional Mean-Variance
Single period– Transaction and market impact costs
– Cannot compare short-term and long-term
Ignores liabilities– Misses contribution patterns
– Risks are asset-only
Assumes symmetric returns
Asset Only Downside Risk Efficient Frontier 5 Year Time Horizon
1
2
3
45
67
89
1011
1
2
3
4
5
6
7
89
1011
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Shortfall Under 6.0000%No
min
al C
ompo
und
Retu
rn
w/out
w/ MITTS & MBS
Model Uncertainties
Simulate Organizationscenarios
Risk aversion
Calibrate and sample
What ifs
Basic Technology
Optimize
Purpose of a Scenario Generator
Construct a representative set of scenarios: plausible paths over planning period – S– Economic factors
– Asset returns
– Liabilities
– Business activities
Use in financial simulator and optimizer
1 2 3 4 ... Ttime
Horizon
Structural models are well placed to support DFA
Company Strategy
Asset Mix Product Mix Capital
Structure Reinsurance
Economic Scenario Generator
Projected FinancialsRisk Profile = Distribution of FutureFinancial Results
Prob
abilit
y
Asset Behavior ModelAsset Behavior Model
Product Behavior ModelProduct Behavior Model
Noise
Noise
Optimization
Inflation Interest Rates Credit Costs Currency
Exchange GDP
Generating Scenarios
Employ stochastic processes for key economic factors:
– interest rates
– inflation
– currencies
Sample with discrete time and discrete scenarios
Examples:
Towers Perrin’s global CAP:Link (Tillinghast TAS)
Calibrated in 21 countries
Siemens Financial Services
Tree generator
Model Uncertainties
Simulate Organizationscenarios
Calibrate and sample Optimize
Corporate Simulations
Project state of company across multi-year horizon– Decisions at beginning each stage
– Uncertainties during periods
– Policy rules guide system
– Iterate over all scenarios
1 2 3 4 ... Ttime
Horizon
Decisions Examples: American Re, Renaissance Re,
Tillinghast TAS-PC
Basic Constructs1 2 3 4 ... T
time
Horizon
Also decisions regarding corporate structure
Asset allocation
Investment Network with Borrowing (each scenario)
STOCK
BOND
LOAN 1
CASH
InterestPayment
InterestPayment
InterestPayment
TerminalNode
Time 1 Time 2 Time 3
Contribution and pay pension benefits
Model Uncertainties
Simulate Organizationscenarios
Calibrate and sample Optimize
Optimization Framework
Surplust = market value (assetst - liabilitiest) Grow economic surplus over planning
period, pay liabilities, reduce insurance costs– t = {1, 2, …, T}– maximize risk-adjusted profit– analyze over representative set of scenarios {S}
Policy constraints, plus risk measures, e.g. sufficient capital to meet 100-200 year losses
Dynamic Optimization Approaches
Dynamic stochastic control (Brennan-Schwartz-Lagnado) relatively simple stochastic model small state-space, few general constraints
Multi-stage stochastic programming (Frank Russell) realistic decision framework, sample scenarios large-size due to # conditional variables
Optimize decision rules (Towers Perrin/Tillinghast) understandable, generate confidence estimates non-convex
Stochastic Programs
1 2 3
time
HORIZON
Xj,ts
Structure of Multi-stage Models
A1
A2
As
Non-anticipativity constraints
scenarios
Optimize over Policy
Decision rules satisfy non-anticipativity conditions Example -- surplus management strategy -- Goals-at-
RiskTM
Intuitive, easy to implement Generates small, highly non-convex optimization problem Employ stochastic program to inspire good decision rules
Non-Convexity
Asset/Liability Efficient Frontier 50 Year Time Horizon
12
3
4
6
7
8
9
10
5
6.5
7.0
7.5
8.0
8.5
9.0
2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42
Ave
rag
e C
om
po
un
d P
ort
folio
Ret
urn
Payout On
Current
Conclusions Multi-period DFA systems are operating today
– Better linkages needed with tactical systems
Customized products will grow from integrated risk management systems
Implementation in various applications– Pension planning– Insurance companies– Coordinated risk management for divisions– Individuals