CYCLES IN CASUALTY:
Balancing Loops in the Insurance Industry
Kawika Pierson
MIT Sloan PhD Candidate
PRESENTATION OUTLINE
The Insurance Industry
 Past Research

Economics
 Control Theory
 System Dynamics
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The Model
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Boundary
Causal Loop Diagram
Important Structures
PID Control
Behavior
How You Can Help
THE INSURANCE INDUSTRY
Basic Idea
 Two Sides to the Business

Insurance
 Investing

Insurance Cycle – What is Cycling?
 Underwriting Loss Ratio or Combined Loss Ratio

Loss Ratio – Adjustments/Premiums
 Expense Ratio – Expenses/Premiums
 Combined Ratio – Loss + Expense = (A + E) / P
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A VIEW TO A CYCLE
A VIEW TO A CYCLE
THE INSURANCE INDUSTRY

Insurance Cycle – What Causes It?
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Industry View:
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“The next stage is precipitated by a catastrophe or similar
significant loss, for example Hurricane Andrew or the
attacks on the World Trade Center.” – “The Insurance
Cycle” wikipedia
Academic View:
“Using quarterly data from 1974 through 1990, we provide
evidence of a long-run link between the general economy
and the underwriting performance as measured by the
combined ratio.” – Grace and Hotchkiss, 1995 J o Risk and
Insurance
 “Fluctuations in the supply of property-liability insurance
may be exacerbated by regulation.” Winter, 1991 Economic
Inquiry
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PAST RESEARCH IN ECONOMICS
Early 1980’s through Mid 90’s
 Three Main Schools of Thought
 Cycle Caused by Interest Rate Fluctuations

Doherty and Kang (1988) – Insurance Prices Change in
Lagged Response to Interest Rates
 Grace and Hotchkiss (1995) – “External Impacts on the
Property-Liability Insurance Cycle”
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Cycle Caused by Limits to the Supply of Insurance
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Winter (1988, 1991, 1994), Gron (1989, 1994)
Cycle Caused by Feedback Processes
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Brockett and Witt (1982) – Loss expectations from the
past inform current premiums, causing autocorrelation
PAST RESEARCH IN CONTROL THEORY
If a Cycle Exists we Will Create a Lagged Negative
Feedback Loop to Explain It
 Balzer and Benjamin 1980 – “Dynamic Response of
Insurance Systems with Delayed Profit/Loss
Sharing Feedback…” Journal of the Institute of
Actuaries
 Zimbidis and Haberman 2001 – “The Combined
Effect of Delay and Feedback on the Insurance
Pricing Process: a Control Theory Approach”
Insurance: Mathematics and Economics
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PAST RESEARCH IN SYSTEM DYNAMICS

The Claims Game and Hanover Insurance
 “claims
management, quality and costs”
 Quality = Claim Adjustment Quality

Daniel H. Kim
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Learning Laboratories
Peter Senge – “The Fifth Discipline”
 Moissis 1989 Masters Thesis (Sterman)
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Focuses on Determining Decision Rules
Cavaleri and Sterman (1997) “Towards evaluation
of systems thinking interventions: a case study”
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Improved Manager’s Mental Models
PAST RESEARCH IN SYSTEM DYNAMICS

Insurance Cycle…
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Are There Really no SD Articles on the Insurance
Cycle?

Thomas Beck
Co-President of Swiss SD Society
 Works for Large Swiss Reinsurer
 No Published Articles on Insurance Cycle
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THE MODEL – BOUNDARY
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Endogenous Variables
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Premiums
Underwriting Quality (Risk)
Claims
Employees
Administrative Costs
Exogenous Variables
Desired Profit Margin
 Size of the Total Market
 Some Components of Administrative Costs
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THE MODEL – BOUNDARY
Many Feedbacks Excluded
 Size of the Insurance Market
 Investments and Interest Rates
 Free Capital’s Influence on Underwriting
 Effect of Time Pressure on Claim Settlement
 Competitive Effects on Profit Margins
 Random Claim Incidence
 Employee Productivity
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Is this Too Far Towards “Negative Loop w/ Delay”
THE MODEL – CASUAL(TY) LOOP DIAGRAM
THE MODEL – STRUCTURES
THE MODEL – STRUCTURES
THE MODEL – STRUCTURES
THE MODEL – STRUCTURES
THE MODEL – STRUCTURES
THE MODEL – STRUCTURES
THE MODEL – STRUCTURES
THE MODEL – PID CONTROL
Translating Equations to SD isn’t Always Easy
 Proportional Control = Standard Structure
 Integral Control = No Steady State Error
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Reasonable that People Use IC
Derivative Control = Less Overshoot
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Less Likely that People Use DC
THE MODEL – PID CONTROL
THE MODEL – PID CONTROL
THE MODEL – PID CONTROL
THE MODEL – BEHAVIOR
Displays Decaying Oscillation to Step Input
Combined Ratio
0.95
0.925
dmnl

0.9
0.8750
0.85
1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010
Time (Year)
Perceived Combined Ratio : Current
THE MODEL – CASUAL(TY) LOOP DIAGRAM
THE MODEL – BEHAVIOR
Instability A Function of Largest Source of Costs
Combined Ratio
0.95
0.925
dmnl

0.9
0.8750
0.85
1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010
Time (Year)
Perceived Combined Ratio : No Admin Cost Change
THE MODEL – CASUAL(TY) LOOP DIAGRAM
THE MODEL – BEHAVIOR

Loop Gain Very Important
Combined Ratio
0.95
0.9
Combined Ratio
0.95
0.8750
0.925
0.85
1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010
Time (Year)
0.9
Perceived Combined Ratio : No Premium Change
dmnl
dmnl
0.925
0.8750
0.85
1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010
Time (Year)
Perceived Combined Ratio : No Premium Change Underwriting Standards Overreaction
THE MODEL – POTENTIAL SOLUTIONS

Derivative Control of Premiums?
Careful Tuning Is Necessary
 Managerial Implementation
 Industry Wide Application
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Why Do Quality Standards Change?
Can This Loop Be Cut
 Life Insurance

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The Kalmanuclear Option?
Optimal LINEAR Filter
 Just Build a Really Good Model Instead
