Minimizing the Cost of Risk With Simulation Optimization Technique

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 simulationbased 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. 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 diversification 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 losses1 or 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,2 defines 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 uncertainty4 defined by Harrington and Niehaus, while the internal and external costs of administering loss control and loss financing programs are comparable to the cost of loss control, loss financing, and internal risk reduction in Harrington and Niehaus's model. …