# Simulation Optimization

APPLICATIONS IN RISK MANAGEMENT[1]

MARCO BETTER AND FRED GLOVER

OptTek Systems, Inc., 2241 17th Street,

Boulder, Colorado 80302, USA

{better, glover}@opttek.com

GARY KOCHENBERGER

University of Colorado Denver

1250 14th Street, Suite 215

Denver, Colorado 80202, USA

Gary.kochenberger@cudenver.edu

HAIBO WANG

Texas A&M International University

Laredo, TX 78041, USA

hwang@tamiu.edu

Simulation Optimization is providing solutions to important practical problems previously beyond reach. This paper explores how new approaches are significantly expanding the power of Simulation Optimization for managing risk. Recent advances in Simulation Optimization technology are leading to new opportunities to solve problems more effectively. Specifically, in applications involving risk and uncertainty, Simulation Optimization surpasses the capabilities of other optimization methods, not only in the quality of solutions, but also in their interpretability and practicality. In this paper, we demonstrate the advantages of using a Simulation Optimization approach to tackle risky decisions, by showcasing the methodology on two popular applications from the areas of finance and business process design.

Keywords: optimization, simulation, portfolio selection, risk management.

1. Introduction

Whenever uncertainty exists, there is risk. Uncertainty is present when there is a possibility that the outcome of a particular event will deviate from what is expected. In some cases, we can use past experience and other information to try to estimate the probability of occurrence of different events. This allows us to estimate a probability distribution for all possible events. Risk can be defined as the probability of occurrence of an event that would have a negative effect on a goal. On the other hand, the probability of occurrence of an event that would have a positive impact is considered an opportunity (see Ref. 1 for a detailed discussion of risks and opportunities). Therefore, the portion of the probability distribution that represents potentially harmful, or unwanted, outcomes is the focus of risk management. Risk management is the process that involves identifying, selecting and implementing measures that can be applied to mitigate risk in a particular situation.1 The objective of risk management, in this context, is to find the set of actions (i.e., investments, policies, resource configurations, etc.) to reduce the level of risk to acceptable levels. What constitutes an acceptable level will depend on the situation, the decision makers’ attitude towards risk, and the marginal rewards expected from taking on additional risk. In order to help risk managers achieve this objective, many techniques have been developed, both qualitative and quantitative. Among quantitative techniques, optimization has a natural appeal because it is based on objective mathematical formulations that usually output an optimal solution (i.e. set of decisions) for mitigating risk. However, traditional optimization approaches are prone to serious limitations. In Section 2 of this paper, we briefly describe two prominent optimization techniques that are frequently used in risk management applications for their ability to handle uncertainty in the data; we then discuss the advantages and disadvantages of these methods. In Section 3, we discuss how Simulation Optimization can overcome the limitations of traditional optimization techniques, and we detail some innovative methods that make this a very useful, practical and intuitive approach for risk management. Section 4 illustrates the advantages of Simulation Optimization on two practical examples. Finally, in Section 5 we summarize our results and conclusions.

2. Traditional Scenario-based Optimization

Very few situations in the real world are completely devoid of risk. In...

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[1] Published in the International Journal of Information Technology & Decision Making, Vol 7, No 4 (2008) 571-587.

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