## 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

OverviewActuarial 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 ModelsDifferent 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 ModelingInsurance 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...

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