Resources on Confidence Level Analysis and Monte Carlo Simulation

Timothy L. Coomer, Ph.D.

A Confidence Level Analysis built using Monte Carlo simulation is a popular technique that every Analytical Broker should be familiar with.  This blog highlights three resources to give you a quick overview of the topic.Loss Simulation Graphic

1.  This graphic gives a quick summary of the topic.  A PDF of this graphic can be downloaded from our resource portal at

2.  As I have mentioned in a prior blog, we are developing training videos for our new resource portal: One of our RISK66® Accelerated Training Videos is on Confidence Level Analysis and Monte Carlo simulation. This video is available temporarily, by clicking here.

3. Finally, included below is a reprint of an article on this subject that was recently published by IRMI.

If you or your clients would like to gain a deeper understanding of how confidence level analysis can be used to support analytical decisions, please contact me at

If you have not already done so, please register for our current portal at Anyone registered for our current portal will be automatically transferred to the new portal when it is launched.


The following article is reproduced with permission of the publisher, International Risk Management Institute, Inc., Dallas, Texas, from Risk Financing, copyright International Risk Management Institute, Inc.  Further reproduction prohibited. For reliable risk and insurance information or to subscribe to IRMI’s free risk management and insurance newsletters, please visit

Analytics:  Teaching Old Methods New Tricks

by Tim Coomer, ARM

Actuarial methods and analytics have been part of the insurance and risk management industry for many decades. With the recent focus on “big data” and business analytics, old methods utilized by actuaries are being employed to tackle an ever-broadening set of decisions. One such technique is the Monte Carlo method. Monte Carlo is a rather romantic sounding name that often includes numerous computational algorithms with one thing in common: repeated random sampling. This issue of Risk Financing Perspectives addresses the expanding interest in analytics and explores a case study where a Monte Carlo technique is used to help a business better understand, holistically, the risk presented by loss retentions across multiple lines of coverage.

The Rise of Business Analytics

A lot can be learned about shifts in business trends and culture by using Google’s Ngram Viewer and search trend analyzer. Basically, these tools reveal how often certain terms have been used in books (back to 1800) and in Internet searches (obviously, more recently). The terms "big data" and "business analytics" have skyrocketed in the past 5 years. "Insurance analytics," a term once used to describe much of the mathematical analyses that occur in the property and casualty insurance industry, has died off quickly. This points to the enterprise-wide application of analytics that is replacing the silo-based approaches of the past. Now, "logistic analytics" and "insurance analytics" all fall under the umbrella of "business analytics." The ability to utilize analytics and data to improve and speed up decision-making has been identified as a new era in business—perhaps as important as the industrial revolution of the 18th and 19th centuries.

Across all industries, there is trickle-down pressure on risk managers to be analytically based and data-driven decision-makers. Chief executive officers (CEOs), shareholders, and boards of directors are all pushing into their organizations the mandate to quickly embrace analytics. A top business journal, The Harvard Business Review, recently quoted Dr. Thomas Davenport of Harvard as follows. "Companies that want to prosper in the new data economy must once again fundamentally rethink how the analysis of data can create value for them-selves and their customers." Analytics are expected to change the competitive landscape for most industries. Risk managers, when surveyed, say internal analytical resources are limited, and 75 percent of risk managers are disappointed with their insurance advisers’ analytical and modeling capabilities. One way to correct this deficit is to self-educate and learn how to apply these techniques to relevant business problems.

The first level of analytics most commonly utilized by an actuary or risk manager is the process of developing loss triangles and loss development factors and then utilizing this information to generate loss projections and reserve analyses. These methods are covered extensively in section II of Risk Financing and typically entail the use of basic mathematics to generate the results. Monte Carlo simulation is a more advanced technique that allows the modeling of more complex scenarios. Monte Carlo is the type of analytical method that can be used in a simplified manner but still provide powerful analyses. There are more advanced Monte Carlo techniques, but this discussion is restricted to a less complex approach.

Monte Carlo

My first opportunity to use Monte Carlo simulation was 30 years ago. At the time, I worked as an engineer with a high clearance level on a project that was part of President Reagan’s Strategic Defense Initiative (SDI or "Star Wars"). I utilized the Monte Carlo modeling technique just as actuarial firms do, for example, in determining loss projections. Obviously, the setting and purpose was quite different. For SDI, I was tasked to simulate what would happen if an enemy missile was launched from the other side of the planet and our military wanted to destroy it before it reached the United States. Typically, such a rocket travels through three phases: the boost phase, mid-course, and terminal. This gives the opposing military three shots at the missile before it reaches its target. Each time a shot is taken, the likelihood of destroying the rocket can be modeled with some type of distribution.

The three distributions, one for each phase of flight, will all be different due to the different capabilities and challenges of targeting and destroying the missile in each phase. The ultimate goal is just to destroy the rocket before it reaches its target. So our interest is in the over-all, combined behavior of these three distributions. Other direct analytical solutions to this challenge can be devised, but there is a richness that emerges from Monte Carlo analysis that cannot be matched with a direct analytical approach. Monte Carlo provides an overall distribution of the likelihood of success. This is a better representation of the entire ballistic defense system and is more insightful than just a single expected value of success or failure.

The beauty of mathematics is that its applicability translates easily across industry boundaries. The SDI modeling effort, just described, is a near perfect match to the modeling of a portfolio effect across multiple lines of coverage. The following example illustrates how such an analysis could assist a chief financial officer (CFO) and/or risk manager in his or her efforts to arrive at an informed decision using analytics.

Case Study: XYZ Company’s Combined Loss Retention

XYZ Company (XYZ) traditionally utilized first dollar coverage to finance insurable losses. However, it recently purchased a workers compensation policy with a $250,000 deductible. After a couple of years of success with the program and seeing substantial savings, the risk manager of XYZ now would like to consider retentions on the general liability including its products liability coverage. However, the CFO is concerned that a large loss in each line of coverage could create a financial hardship for the organization. Obviously, the likelihood of a maximum loss on each line of coverage is unlikely. To assist with the decision-making process, a quantitative analysis of the risks is undertaken.

Just as with the SDI example, the three lines of coverage represent three different probability distributions. It is the combined distribution that is of interest to us and this can be modeled using a Monte Carlo technique. The options under consideration and the three separate distributions as represented by a confidence interval analysis are shown in Table 1.

Table 1: Loss Distribution for Different Lines of Coverages

Table 1

Note that the aggregate loss probability column indicates the level of confidence that losses will not exceed the aggregate loss amount shown for each line of coverage.

Table 2 compares a straight aggregation of the three distributions to the combined portfolio effect using a Monte Carlo technique. The Monte Carlo generated distribution provides a much better estimate of the likelihood of loss across all lines of coverage. The aggregated and Monte Carlo distributed distributions are similar until the 75th percentile, where the Monte Carlo technique shows the portfolio effect and the decreased likelihood that all lines of coverage would experience loss levels high in the confidence interval.

Table 2: Straight Aggregation of Loss Distributions versus Monte Carlo Technique

Table 2

By interpreting this table, the risk manager can express confidence that 90 percent of the time, the losses retained by the organization will be$3,540,000 or less. This is $660,000 less than the straight aggregation of all distributions and may have an impact on the retention decision made by the CFO and risk manager.

Monte Carlo techniques are utilized in a variety of scenarios and provide a useful analytical tool for mathematical modeling across a diverse range of industries. In the above example, you can clearly see the challenge of understanding the combined risk represented by three distinct retentions and the much-improved insight created by the single combined Monte Carlo distribution.




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