Actuarial Models

Actuarial models are the tools that actuaries use to represent or simulate future contingent events. A contingent event is one in which its timing and severity is unknown. Contingent or risky events cannot be avoided with 100% certainty; the best that can be done to mitigate the effects of risk is to insure against its financial impact. Actuaries conduct analyses using historical data to predict the likelihood that a future event will occur. Variables, which are characteristics of a certain entity set, are used as inputs into actuarial models to approximate the behavior of reality. Common variables used in actuarial models include: Age, gender, marital status and zip code. Common variables help to predict with some accuracy the outcome of some actuarial models. Today, actuarial models are using more complex variables and a larger number of variables to model future outcomes. Data mining of large databases allows actuaries to build complex predictive models. Predictive models look for pattern matching or correlations between data points; these correlations allow actuaries to model complex realities that were never before possible. Some of the applications that are emerging as a result of predictive analytics are offering strategic advantage to companies who use these powerful models to plan for future risk events and their financial impact. Value-based actuarial models and predictive analytics for identifying insurance claims fraud are two examples of how actuarial models are evolving into powerful tools that offer a competitive advantage in the marketplace.

Keywords Decile Management; Descriptive Modeling; Insurance Fraud; Predictive Analytics; Predictive Modeling; Synthetic Variables

Actuarial Statistics > Actuarial Models

Overview

Actuarial models make projections about future events that may or may not occur. Actuarial models primarily use historical data (what has happened in the past) to simulate what is likely to occur in the future, and the models rest upon assumptions (variables) concerning the future. Actuarial findings/outcomes of modeling processes are estimates and not a guarantee of a particular outcome. All models are simulations of future events.

The statements above should give the reader a good idea about the reliability of actuarial models in predicting the future likelihood of an event. Actuaries can't and won't guarantee the outcomes of their models as the gospel truth. Instead, actuarial models attempt to represent a close approximation to what is likely to occur based upon what has happened in the past.

There are usually financial implications associated with actuarial risks. Actuaries who develop and implement models don't profess to have a crystal ball into the future. A scientific model is an abstract and simplified representation of a given phenomenon ("The roles of the actuary," 2006).

The following are true of actuarial models ("The roles of the actuary," 2006):

• Models are a mathematical representation of contingent future events.
• Models are simulations.
• Models approximate the behavior of reality.
• Models have predictive power — they don't represent truth.
• "Simple laws don't not adequately describe complex realities."

Actuarial research provides a means to test the validity and appropriateness of hypotheses and assumptions. An actuary conducts the following steps that involve the preliminary validation of data and statistical analysis required in building a model ("The roles of the actuary," 2006).

• Record observations
• Apply theoretical and practical understanding of how risks operate
• Make observations of actual experience-these represent the primary facts
• Apply hypotheses and assumptions.

Actuarial Models can be either simple or complex. An example of a simple model might be the actuaries' calculation of a single interest rate projection on monetary value. A complex model might analyze all material aspects of business operation in an effort to estimate future financial viability. A complex model typically permits long range projections and adjustments are made periodically ("The roles of the actuary," 2006). Complex models are utilized often by today's actuaries; powerful computer technology allows actuaries to apply many variables in models and run scenarios very efficiently.

The refinement of a model happens when the actuary compares the results of running the model to actual events. A number of scenarios are run using the same model with different assumptions or simulation techniques. In many cases, different models are used to simulate a variety of outcomes. The outcomes are analyzed and the models are run again. This feedback loop tends to improve the model's output in terms of its ability to accurately represent the real world — which in turn does a better job of predicting future outcomes. "Expecting certainty from an actuarial model effectively makes the model useless since it provides no additional information about the anticipated event. Therefore, actuarial models do not and cannot predict the future with certainty" ("The roles of the actuary," 2006).

Outcomes of Different Models

Different models with different input assumptions will produce outcomes that are different. For this reason, a model that produces results that when analyzed are closer to actual real outcome, the model should not be considered correct or more accurate; the results of the model are dependent upon a number of factors and not just the model itself

In fact, actuarial models are sensitive to assumptions and assumptions change. The historical experience upon which assumptions are based is changeable. In fact, historical experience is potentially a poor base for making future projections because legal, social and economic changes occur with regularity.

Actuarial models are designed to take into account events that are more likely to occur on average and not infrequently occurring events such as catastrophic events. Actuarial models are highly dependent upon the availability of valid data. The outcomes of models are probabilistic in nature and can never be assumed to provide more than estimates of possible outcomes through their implementation. It is now clear to the reader that actuarial models do not predict future events with certainty. Actuarial models simply serve as tools to model the financial risk associated with many different scenarios. This essay describes several business applications for actuarial models including: Value-based models and fraud detection models. The use of predictive analytics as the foundation of many of today's key risk/reward decisions is discussed.

Applications

Predictive Modeling

Insurance companies operate very unique business models. Most businesses produce goods and services which are sold to customers for immediate use. Insurers, on the other hand, sell products without knowing how much the product will cost to produce. Insurers make guesses about future costs; if an insurer guesses incorrectly, the company could lose customers or it could go out of business. Predictive modeling is the best tool that insurance companies have at their disposal to predict how much to charge for their products (policies). Insurance companies have long been subject to much regulatory oversight as an industry and for this reason, insurers have relied on relatively simple models and methods to model risk premiums. Insurance companies like all for-profit businesses, operate with the goal of making money. Without innovative products and services, insurers operate in the middle of the pack and often struggle to make a profit.

Because insurance companies collect premiums today for payouts in the future, it is critical for policy holders to know that their insurer will be around to settle claims — even if the claims won't be realized for years or decades. Softening markets are spurring insurers to grow market share, premium base and product diversification (Amoroso, Lucker, Marino & Zizzamia, 2006). Because of the nature of insurance and because of increasing risk in general, insurers must adopt predictive tools to insure their solvency and show their commitment to customers. Insurers use predictive modeling in four general business areas ("Predictive modeling," 2007):

• Actuarial
• Marketing
• Underwriting

• Claims

Predictive modeling incorporates random variables to generate scenarios; each scenario is assigned a risk score. Risk scores are associated with applicable business rules; knowing the relative risk associated with a key business decision or initiative enables companies to prioritize enterprise risk. In today's highly competitive business environment, business decisions must be actionable, defensible, and measurable. The scores or weights that actuaries assign to risks are being tied to business rules to insure that risk analysis impacts the appropriate area of business operations. Decile management is the process of assigning risk to appropriate business segments. Actuaries drive the data behind decile management by implementing the following ("Advanced analytics," 2007):

• Identifying the best combination of risk characteristics.
• Determining the ideal weight for each characteristic relative to others (the results of weighting should be usable, repeatable and executable).
• Analyzing risk which allows for pricing each and every risk: Risk will be segmented in varying markets and conditions.

Generic business models don't offer competitive advantage but developing customized models using internal, external and synthetic data can offer huge advantages to insurers through the development of innovative and cost-competitive products.

Analytics & Underwriting

Underwriting decisions have characteristically had a subjective component which leads to great variability and pricing. The implementation of predictive models offers ("Advanced analytics," 2007):

• Statistical soundness
• Objectivity
• Consistency in methods

Predictive models rely on the careful examination of historical data to identify patterns; new modeling solutions need to be able to digest an ever increasing list of variables to support segmentation and competitive risk pricing. Synthetic variables are new underwriting characteristics which are imbedded in the voluminous data that many actuaries analyze everyday. The analysis of synthetic variables is beyond the capability of the actuary and traditional statistical analysis. However, with the development of sophisticated software applications and computer calculations, these variables can be extracted through data mining. Predictive models allow for increased automation and allow underwriters and actuaries more time to view risk that cannot be reviewed automatically ("Advanced analytics," 2007).

Predictive models have proven successful in property and casualty insurance lines, healthcare, professional liability and medical malpractice. Predictive models are expanding as analytic tools for non-insurance business such as consumer business, financial services and human resources management. Nearly all business processes can be beneficially impacted by data mining and predictive modeling because the use of predictive models allows for:

• More accurate pricing of each risk
• Reduction in losses
• Maximization of profits

Issues

Value-based Design & Actuarial Models

Employer sponsored health care plans are a core benefit at many companies; employers have always wanted to get the greatest value for their money while containing health care costs. As medical costs rise, many companies have shifted more of the burden of health care costs to employees. A prime example of this can be illustrated in the increasing co-pay amounts that employees must pay for prescription drugs. On the surface, cost sharing seems to make a lot of sense; as health care costs rise, sharing expenses gives more responsibility to employees to spend dollars wisely or adopt healthier lifestyles. Unfortunately, there's evidence that across the board increases in prescription drug co-pays actually reduces the likelihood that employees will use essential medications ("You want to be healthy," 2007).

There's compelling evidence that people with certain medical conditions do much better from an overall health standpoint if they comply with specific medical directives. One example that clearly illustrates the value of patient compliance can be seen in the treatment of diabetes. According to Jennifer Boehm, a principal at Hewitt Associates: "There are certain things that we know based on medical evidence. For instance, diabetics need to be compliant with their medications as well as doing other things, such as getting their eyes examined, to manage their chronic condition. If not, they are going to be out of work more often, and they might have to deal with circulatory issues down the road" ("New actuarial model," 2007). It is well documented that a diabetic who forgoes taking his medication is likely to suffer more serious and much more expensive health-related issues than a diabetic patient that takes his medication. Employers have implemented many strategies to keep patients healthy (including: education, on-site medical and in-house wellness programs) but health care costs continue to rise.

Development of Value-based Actuarial Models

Hewitt Associates collaborated with two doctors; Mark Fredrick MD (University of Michigan) and Michael Chernew PhD (Harvard Medical School) in the creation of a new actuarial model that would help companies assess the financial impacts related to cost sharing of health care services. In other words, the actuarial model that was developed would analyze an employer's data about drug utilization and costs, and allow companies to make changes to their health care plans that would in turn result in "clinically desirable" outcomes ("New actuarial model," 2007).

The following questions are difficult to answer without the ability to input a number of variables into an actuarial model:

• What affect does increasing co-pay have on employee health outcomes?
• Should co-pay amounts be uniform across all health services?
• What compliance issues are necessary to track for reducing overall health care costs? What are the correlations between treatment and subsequent diseases and complications?
• Where can financial resources be shifted that will have the least impact — reducing or maintaining health care costs.
• What are the cost implications associated with make different decisions related to employee health care benefit programs?

The questions above are not easy to answer without the use of the value-based actuarial model described here. Value-based actuarial models can create "what….if" scenarios that help analysts understand the cost impact of prescription drug plan changes. The bottom line seems to be that as co-pays rise, people are less likely to buy their prescriptions. If a co-pay is reduced to $0.00 for a diabetic person and he takes his medicine, all indications from the models are that the employer will actually save money in health care costs.

The Hewitt tool allows employers to be more selective in how they set their benefit design package. "It's taking the dollars that an employer has and allocating them in the right places-places that have the greatest value," says Sara Teppema, a lead development actuary at Hewitt. Moreover, she adds, value-based design needs to be looked at in terms of the client's overall healthcare strategy and total health-risk management strategy: "What [is the company] doing to incent healthy behavior, wellness, lifestyle changes?" ("You want to be healthy," 2007).

Fraud Detection & Predictive Modeling

Another area where actuarial models are getting a lot of use is in the area of detecting fraudulent insurance claims. Fraudulent claims submitted to insurers cost millions each year. Dealing with fraud increases operational overhead and ultimately cost policy holders in the form of higher premiums. Insurers have always been aware of the impact that the filing of fraudulent claims has had on their line of business, but until the advent of computer technology and access to digital archives, their recourse has been limited. Identifying fraudulent claims before they are paid can reap huge benefits for insurers. For insurer Aetna, the benefits of using an actuarial model to detect patterns of fraud claims are obvious. Aetna says that by using an actuarial model to detect patterns of potential claims abuse, the company was able to stop $89 million in payments from going out the door. Previous to using the model, Aetna was only able to recoup $15 million that had been paid out in fraudulent claims. "Companies can save far more money by stopping claims before they are paid than by trying to get fraudsters to pay back money" (Appleby, 2006).

Insurers feel intense pressure to pay claims quickly which means that it is becoming increasingly difficult for manual claims processing to pick up on fraudulent claims early in the process. Insurers need an automated way to review and reconcile claims quickly while checking claim data for red flags that might signal potential fraud. Actuarial models help insurance companies combat fraud and process claims more accurately and quickly than can be done in person. Pre-payment fraud protection is really in its infancy; most insurers do audits after claims payments are made but by that time, it is often difficult or impossible to recoup the claim dollars. Predictive models using pattern matching are becoming an indispensable tool for many insurance providers. A 2006 survey reported that of 55 private insurers, 70 percent were using anti-fraud software systems (Appleby, 2006).

Much of fraud detection still relies on "static" checks such as exception checking and rules-based systems. The problem with static checks is that they are not good at responding to the "subtle" patterns and relationships that indicate fraudulent behavior. Data mining involves building models that capture behavioral patterns which are detected when they are run (O'Flattery, 2005). There are two types of actuarial models that are used as a means of fraud detection. They are:

• Descriptive Models: This type of model simply looks for patterns within data. Similarities between claims or the frequency of an occurrence with another event are identified and are reviewed further to validate assumptions. This type of model doesn't benchmark its outcomes against known events, but rather gives analysts insights into correlations; some of which may be indicative of fraudulent activity.
• Predictive Models: The building of a predictive model takes place in two steps. First, the model is built using claim data that includes confirmed data that is fraudulent. The model "remembers" patterns and then the model can be applied to new "clean" data where the model identifies similar patterns. Depending upon the correlation and similarity of patterns, a score is assigned indicating the likelihood of fraud.

Most insurers don't have access to historical fraud data that is required to build predictive models. Therefore, many insurers are getting started by developing and using descriptive models to identify anomalies (O'Flattery, 2005).

Everyone agrees that fraud and the associated costs greatly impact an organization's bottom line. Insurers generally group fraud into two categories; opportunistic and planned. Established information exchanges can support predictive models and the sharing of known patterns of fraud allow for identification of such patterns. Predictive models are better tools for identifying "planned" fraud, but some contend that its weakness lies in the fact that they focus in on past behaviors. Knowing what fraud has occurred has proven valuable in pinpointing suspect activities, but what insurers really need are tools that prove fraud — not just its likelihood (Smith, 2004). The question really remains, will predictive models ever be able to accurately identify the actual occurrence of fraud with the speed and accuracy that many insurers say is vital to supporting their business needs? Many insurers are worried that implementing fraud detection systems, while a necessary evil, could create suspicion and negativity between insurers and policy holders. Insurers need to tread lightly where customers are concerned. Claims need to be paid quickly and customer service has never been more important to retaining policy holders. Limiting fraudulent claims will be a benefit to insurers and customers; from a public relations standpoint, it is a strategy that must be pursued (Smith, 2004). Estimates put the number of fraudulent claims at between 10 percent to 15 percent of all claims submitted; traditional claims review processes cannot handle the increasing rate of fraudulent claims. The challenge really is to identify fraud early in the claim process and technology can help. The complexity of claims must be determined and prioritized, so that workflow processes can be implemented. Workflow processes also need to assign time limits to claims to insure that claims are dealt with in a timely and legal manner (Tallaksen, 2007).

Actuarial models are built to accept data as inputs; the more complete and accurate the data inputs, the better representative are the outcomes of the model. As a precursor to the descriptive modeling process, there are steps that can be taken to insure later and better success for future models. Some of the simplest steps involve the compilation of complete, integrated policy information. Data must be complete and as accurate as possible. It must be organized in such a way that it is placed into a context with other related data. As actuarial models become more complex, the quality and integrity of data is becoming more important as well. "Company data is being acknowledged as the largest off-the-balance sheet asset" (Amoroso, Lucker, Marino & Zizzamia, 2006). Data accuracy and quality will be increasingly valuable as a repository of strategic advantage. Companies will need to be committed as never before to searching for and obtaining new data sources and risk characteristics within the data.

Terms & Concepts

Automated Underwriting: The process by which risk premiums are assigned automatically through the evaluation of assumptions and models; review of claims doesn't involve a human being to review the claim.

Contingent Event: An event that's occurrence, timing and severity is uncertain.

Decile Management: The ability to accurately and objectively price risks across all risk segments.

Descriptive Modeling: The process by which correlations and patterns are detected in databases.

Loss Control: The process of applying management practices, knowledge, and technical skills to develop, enhance, and implement risk avoidance, loss prevention, and loss reduction.

Pattern Matching: A technique in automated data analysis, usually performed on a computer, by which a group of characteristic properties of an unknown object is compared with the comparable groups of characteristics of a set of known objects, to discover the identity or proper classification of the unknown object (Free dictionary, 2008).

Predictive Analytics: A branch of data mining that predicts future probabilities and trends. Predictive analytics uses a variable that can be measured for an individual or other entity to predict future behavior.

Predictive Modeling: The careful examination of historical data to identify patterns. The patterns are then applied to other data to identify similar patterns.

Random Variables (aka: Actuarial Assumptions): The rule that assigns a numerical value to every possible outcome.

Synthetic Variables: Variables that can be identified only by computer analysis as it is too complex to be identified easily by human analysis.

Underwriting: The process of evaluating an insurance policy to determine the amount of risk involved for the insurer.

Bibliography

Appleby, J. (2006, November 7). Computer programs help flag insurance fraud before payment. USA Today. Retrieved January 15, 2008, from http://www.usatoday.com/tech/news/computersecurity/2006-11-07-medicare-side-usat%5fx.htm

Advanced analytics and the art of underwriting. (2007). Deloitte Touche Tohmatsu. Retrieved January 14, 2008, from http://www.deloitte.com/dtt/cda/doc/content/dtt%5ffsi%5fTheArtOfUnderwriting%5f20070102.pdf

Amoroso, R., Lucker, J., Marino, J. & Zizzamia, F. (2006). Secrets to successful commercial segmentation. Best's Review, 107(3), 86-89. Retrieved January 14, 2008, from EBSCO Online Database Business Source Premier. http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=21612567&site=ehost-live

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New actuarial model seeks to quantify cost impact of value-based designs. (2007). Managed Care Outlook, 20(19), 1-5. Retrieved January 14, 2008, from EBSCO Online Database Business Source Premier. http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=26765696&site=ehost-live

O'Flaherty, K. (2005). Fraud detection through data mining. Claims, 53, 10-10. Retrieved January 14, 2008, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=17302806&site=ehost-live

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Pyenson, B.S., Sander, M.S., Jiang, Y., Kahn, H., & Mulshine, J.L. (2012). An actuarial analysis shows that offering lung cancer screening as an insurance benefit would save lives at relatively low cost. Health Affairs, 31(4), 770-779. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=75375397&site=ehost-live

Richards, S.J. (2012). A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal, 2012(4), 233-257. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=84342497&site=ehost-live

Smith, G. (2004). Combating fraud with quality. Canadian Underwriter, 71(9), 52-59. Retrieved January 14, 2008, from EBSCO Online Database Business Source Premier. http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=14744518&site=ehost-live

Tallaksen, T. (2007). Electronic claim tools. Claims, 55(5), 56-58. Retrieved January 14, 2008, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=25249909&site=ehost-live

The roles of the actuary in the selection and application of actuarial models. (2006). Actuary.org. Retrieved January 13, 2008, from http://www.actuary.org/pdf/prof/models%5fjune06.pdf

You want to be healthy, but at what price? (2007). Treasury & Risk. Retrieved January 16, 2008, from http://www.treasuryandrisk.com/topic/benefits/1074

Suggested Reading

Connolly, J. (1999). NAIC exposes actuarial opinion model draft. National Underwriter, 103(41), 6. Retrieved January 17, 2008, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=2387474&site=ehost-live

Linnemann, P. (2003). An actuarial analysis of participating life insurance. Scandinavian Actuarial Journal, 2003(2), 153. Retrieved January 17, 2008, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9913797&site=ehost-live

Pyenson, B. S. (1997). Using actuarial models to assess managed care risk. Healthcare Financial Management, 51(1), 35-37. Retrieved January 17, 2008, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9711141068&site=ehost-live