Modeling requires, in addition to technical skills, a broad background
that includes knowledge in areas such as regulation, political science,
marketing, sociology, psychology, history, and even literature.
interest in turn is a function of the amount in the account and
the interest rate, both with positive polarities.
The mathematical representation of the stocks (in the stocks
and flow) is straightforward:
Investment Incomei = Interest Ratei × Account Valuei
and
AccountValuei = Account Valuei– 1 + Investment Incomei
Fundamental Patterns of Dynamic Behavior
Because each complex situation that is modeled using system
dynamics generates its own causal map, you might think that
the range of behavioral patterns is infinite—or, at least, huge.
But it turns out there are only six fundamental patterns, three
of which are illustrated below:
■ ■ Exponential Growth—Figures 1 (reinforcing loop) and 4 (
account value) result in exponential growth as shown in Graph 2;
■ ■ Oscillation—Figure 2 (the underwriting cycle) results in oscillation as shown in Graph 3. As a matter of fact, in its most
fundamental form, oscillation requires only one balancing
loop with time delay (Figure 2 depicts two balancing loops);
■ ■ Growth with an Overshot—Graph 4 depicts growth with an
overshot, which—in its most fundamental form—requires
only one reinforcing loop and one balancing loop with delay.
The deceptively simple but fundamental conclusion is that
system structure determines system behavior. With this knowledge we can explain, for example, why modeling infectious
disease is similar to modeling fads and fashion—their causal
maps are actually quite similar.
Effect of births and Deaths on the Population
Deaths
Outflow
2,000
2,100
2,205
2,315
2,431
2,553
2,680
2,814
2,955
3,103
Time
1
2
3
4
5
6
7
8
9
10
Births Inflow
4,000
3,900
3,803
3,707
3,615
3,524
3,436
3,350
3,267
3,185
Population
102,000
103,800
105,398
106,790
107,973
108,945
109,701
110,237
110.549
110,631
Return on Value
Given that well-constructed models confer a strategic advantage to those who are making decisions, it’s fair to ponder the
value of devoting resources to their construction. To answer this
question, it’s important to remember that system dynamics is a
tool for modeling dynamic complexity in systems that exhibit
APPLICATIONS, ANYONE?
SYSTEM DYNAMICS hAS bEEN uSED to tackle a
variety of corporate strategy and public policy
issues, including:
■ ■ Simulating project management;
■ ■ understanding the consequences of urban
planning on traffic congestion;
■ ■ Assessing the impact of the life cycle on product
innovation;
■ ■ Modeling market fads or business cycles;
■ ■ Managing business growth;
■ ■ Re-engineering the supply chain;
■ ■ Predicting oil prices;
■ ■ optimizing capital and labor;
■ ■ uncovering path dependence;
■ ■ Forecasting the demand for landline and mobile
telephone service;
■ ■ Studying the Cold War arms race between the
united States and the former Soviet union;
■ ■ Forecasting the evolution of the hIv/AIDS
epidemic;
■ ■ Capturing morale and productivity in
organizations.
Applications of interest to actuaries could
include designing insurance exchanges, assessing
the impact of regulation on profitability, managing
long-term disability and long-term care businesses,
investigating stop-loss pricing in light of the
underwriting cycle, building predictive models
that don’t rely on data mining, and assessing the
effects of the current study system on the actuarial
profession’s financial outlook.
