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

The Model 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

A VIEW TO A CYCLE

A VIEW TO A CYCLE

THE INSURANCE INDUSTRY

Insurance Cycle – What Causes It? Industry View:

“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

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”

Cycle Caused by Limits to the Supply of Insurance Winter (1988, 1991, 1994), Gron (1989, 1994)

Cycle Caused by Feedback Processes 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

PAST RESEARCH IN SYSTEM DYNAMICS

The Claims Game and Hanover Insurance“claims management, quality and costs”Quality = Claim Adjustment Quality

Daniel H. Kim Learning Laboratories Peter Senge – “The Fifth Discipline” Moissis 1989 Masters Thesis (Sterman) Focuses on Determining Decision Rules Cavaleri and Sterman (1997) “Towards evaluation

of systems thinking interventions: a case study” Improved Manager’s Mental Models

PAST RESEARCH IN SYSTEM DYNAMICS

Insurance Cycle…

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

THE MODEL – BOUNDARY

Endogenous Variables Premiums Underwriting Quality (Risk) Claims Employees Administrative Costs

Exogenous Variables Desired Profit Margin Size of the Total Market Some Components of Administrative Costs

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

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

Reasonable that People Use IC Derivative Control = Less Overshoot

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

0.9

0.8750

0.851950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010

Time (Year)

dmnl

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

0.9

0.8750

0.851950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010

Time (Year)

dmnl

Perceived Combined Ratio : No Admin Cost Change

THE MODEL – CASUAL(TY) LOOP DIAGRAM

THE MODEL – BEHAVIOR

Loop Gain Very ImportantCombined Ratio

0.95

0.925

0.9

0.8750

0.851950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010

Time (Year)

dmnl

Perceived Combined Ratio : No Premium Change

Combined Ratio

0.95

0.925

0.9

0.8750

0.851950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010

Time (Year)

dmnl

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

Why Do Quality Standards Change? Can This Loop Be Cut Life Insurance

The Kalmanuclear Option? Optimal LINEAR Filter Just Build a Really Good Model Instead