Minimizing the Cost of Risk With Simulation Optimization Technique

• Published date: 01 March 2011
• DOI: http://doi.org/10.1111/j.1540-6296.2010.01193.x
• Author: Yu Lei
• Date: 01 March 2011

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Risk Management and Insurance Review, 2011, Vol.14, No. 1, 121-144

DOI: 10.1111/j.1540-6296.2010.01193.x

EDUCATIONAL INSIGHTS

MINIMIZING THE COST OF RISK WITH SIMULATION

OPTIMIZATION TECHNIQUE

Yu Le i

ABSTRACT

For risk managers, one overarching goal is to help their organizations maximize

stakeholders’ value, which can be achieved by minimizing the cost of risk.

Oftentimes such optimization decisions have to be made under uncertainty.

This article presents a teaching note that demonstrates how to use simulation-

based software to run optimization involving uncertain factors. Specifically, a

hypothetical example regarding workers’ compensation claims cost was created

to provide a step-by-step instruction for conducting simulation optimization.

INTRODUCTION

One common goal for risk managers, regardless of the industry they are in, is to help

their respective organizations achieve their mission, which is to maximize stakeholders’

value. Harrington and Niehaus (2004) present a simple model that shows that value

maximization is equivalent to cost minimization. The model assumes the following

form:

Value with risk =value without risk −cost of risk.

In other words, a firm’s value in a risky world is the difference between the hypothetical

value of the firm in a risk-free world and the cost of risk.

According to Harrington and Niehaus (2004), “as long as costs are defined to include all

the effects on value of risk and risk management (RM), minimizing the cost of risk is the

same thing as maximizing value” (p. 22).

Harrington and Niehaus (2004) think there are five components of the cost of risk,

namely:

1. Expected losses

This component includes the expected cost of both direct and indirect losses.

2. Cost of loss control

This component includes any money spent to reduce the frequency and/or severity

of accidents.

YuLei is Assistant Professor of Insurance, Barney School of Business, University of Hartford, 418

Auerbach, 200 Bloomfield Avenue, West Hartford, CT 06117; phone: 860-768-4682; fax: 860-768-

4911; e-mail: lei@hartford.edu. This article was subject to double-blind peer review.

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3. Cost of loss financing

This component includes the cost of self-insurance, insurance premium loadings,

and any transaction costs in arranging, negotiating, and enforcing noninsurance

transfer contracts.

4. Cost of internal risk reduction

This component includes costs spent on internal risk reduction such as diversifi-

cation across product lines or geographical areas,

5. Cost of residual uncertainty

This component covers any potential cost associated with any residual uncertainty

that cannot be eliminated through loss control, loss financing, and internal risk

reduction.

The goal for risk managers is to minimize the total cost of risk, which is the sum of the

above five components, not any single component of it.

It is not always easy to identify and quantity all elements of the total cost of risk, though.

For instance, the true cost of indirect losses1or residual uncertainty is particularly

difficult to measure. Harrington and Niehaus (2004) acknowledge such difficulty but

point out that the cost of risk concept is used extensively in practice and helps companies

facilitate categorization of the major ways that risk reduces value.

Because of the practical limitations in measuring certain elements of the total cost of

risk, businesses often will not attempt to include all effects on value of risk and risk

management in their calculation of the total cost of risk. Instead, companies look at the

total cost of risk more from an insurance purchaser’s point of view. For instance, in its

annual benchmark survey, The Risk and Insurance Management Society,2defines the

total cost of risk as being made up of insurance premiums, retained losses (including

insurance deductibles and self-insured retentions), and internal and external costs of

administering loss control and loss financing programs.3

The Risk and Insurance Management Society’s calculation of the total cost of risk is in

line with Harrington and Niehaus’s (2004) model. The insurance premiums and retained

losses together would approximately correspond to the sum of expected losses and cost

of residual uncertainty4defined by Harrington and Niehaus, while the internal and

1Such as potential damage to reputation and additional money spent to find and train replace-

ment workers in work-related injury cases.

2The Risk and Insurance Management Society is a New York–based not-for-profit organization

dedicated to advancing the practice of risk management. Since 1979, it has coproduced an annual

survey with various partners that risk management professionals can use as a benchmarking

tool to compare their organizations’ total cost of risk against that of their competition. Its

2009 survey covers industry data from nearly one-third of the Fortune 500 companies and 70

industry categories. See http://www.rims.org/Pages/Default.aspx for more details about the

organization and its annual survey on the cost of risk.

3The Risk and Insurance Management Society credits its former President Douglas Barlow with

developing this in 1962.

4Retained losses may be considered a proxy for the cost of residual uncertainty in Harrington

and Niehaus’s (2004) model.