Risk Theory & Credibility Research Paper Starter

Risk Theory & Credibility

(Research Starters)

Risk theory and credibility can most easily be understood by breaking the topic down into two components: Risk theory and credibility theory. Both topics are theories studied by actuaries and insurers; risk theory deals with the financial impact of risk on an insurer's overall insurance portfolios (product offerings). Credibility theory was originally developed as a means of determining insurance rates as they related to the risks associated with the groups being insured. In today's complex insurance industry, risk theory and credibility encompass similar concepts, but in many cases the terminology associated with risk assignment and premium calculations has changed. Many newer terms associated with risk and credibility are introduced and defined in this essay. Actuaries have sophisticated databases of information about policy holders and groups that were only dreamed about when risk theory was in its infancy. In addition to vast data repositories of information and criteria about groups, actuaries also employ sophisticated computer formulas and models to calculate risk with ever increasing accuracy. Rate making is the common term for calculating the price of an insurance premium for a particular group (and its associated risk). The ability to calculate insurance premiums that are adequate, reasonable and fair encompasses many factors. These factors include: Calculating appropriate risk for the insured, keeping rates competitive and ensuring availability of insurance coverage (non-discrimination against groups). Other factors include reliance by insurers on sophisticated risk models that are able to predict catastrophic risk without having access to years of historical data that is typically used in traditional predictive analysis. Insurance companies are also being required to have on hand adequate financial reserves to be able to cover catastrophic losses. Insurance companies can bolster capital reserves by buying reinsurance or financing risk through investment vehicles such as catastrophic bonds. If insurance companies are not able to secure adequate capital reserves to cover large risks, they may be forced to drop out of some insurance markets-leaving policy holders with fewer or no options for insurance coverage.

Keywords Actuary; Credibility Theory; Experience Rating; Long Tail Insurance Event; Rate Making; Rating Agencies; Reinsurance; Risk Models; Risk Theory; Risk-Reward Relationship; Short Tail Insurance Event; Third Party Model or Product (Risk Models)

Actuarial Science: Risk Theory


To many individuals and organizations, insurance is thought of as an unavoidable but necessary expense. In theory, we all understand that insurance is a way to protect ourselves, our families and our assets from loss caused by unforeseen future events. Because insurance is acquired to mitigate the risk of illness, theft, fire or other "disasters," the entire idea of insurance has a rather unpleasant connotation to many.

In fact, insurance is a tool that individuals and businesses use to manage financial risk. In other words, an insurance policy transfers risk from an individual or business and onto an insurance company in return for a premium payment. An insurance company assumes risk for policy holders which may at first seem to be an altruistic act; however, insurance companies are businesses that are focused on making money and remaining solvent.

Risk Theory

Insurance risk theory has historically dealt with a number of factors. From the insurer's standpoint, risk theory encompasses the following:

  • Analysis of risk for given populations or classes (policy holders).
  • Determination of insurance premium rates.
  • Reinsurance required to mitigate risk for primary insurers.
  • Defining how much capital to reserve to cover potential claims.

Much of the risk that insurance companies assume for policy holders is somewhat predictable. Insurance companies use predictive modeling that analyzes data and trends from many previous years' data. "For short tail insurance risks such as property, motor damage and theft, and for common forms of loss such as those arising from theft, building fire, accident, and small to moderate storm damage, the risk is generally estimated from loss records" (Walker, Garnder, & Johnstone, 2004).

If all risk could be modeled in this manner, insurance companies would have a much easier time in predicting how many claims were likely to be paid and how much money would need to be kept in reserve to pay claims, meet operation expenses and ensure profitability. Risk models for catastrophic risks related to natural disaster or acts of terrorism have proven to be deficient or just plain wrong. The insurance industry is responding by developing new risk models for these types of events.

"The risk of large losses from catastrophic events such as earthquakes and tropical cyclones is based on complex computer models utilizing geographic information systems (GIS) technology that simulate a large number of events representative of what would be expected over thousands of years. Actuarial techniques involving triangulation have been developed to estimate the long tail insurance risks that are characteristic of casualty insurance" (Walker, Garnder, & Johnstone, 2004).

Actuaries have historically focused on the analysis of risk to determine premiums; the technological advances in data storage, data mining and computing are transforming risk management in the insurance industry. With sophisticated data mining tools, it is possible to track an enormous number of variables related to policy holders. It is now possible for insurers to segment populations with greater and greater precision; therefore allowing insurers to assign risk more accurately.

Insurance companies manage risk by transferring policy holder risk to other insurance companies and reinsurance companies. Transferring and dispersing risk is founded in the "central limit theorem." The mathematical basis of this risk transfer (also known as law of large numbers) facilitates the interaction between risk, capital and solvency, provided that there is sufficient knowledge about the risk (Walker, Garnder, & Johnstone, 2004).

As Walker, Gardner, and Johnstone explain, “A primary requirement of an insurance company is that it should be sustainable into the future in terms of both returns to the shareholder and solvency. If a company has a target average annual rate of return on equity and a maximum risk of insolvency which it wishes to achieve over, for example, the next 10 years, then these systems can be used to determine the optimum premium rates, investment strategy and reinsurance programs to do this” (2004).

Insurers need to maintain adequate financial capital to meet their obligations in terms of paying claims as well as to maintain solvency. In 1992, Hurricane Andrew ruined a record number of insurers that didn't have adequate capital reserves in place. Rating agencies, which assign solvency risks to insurers, are working to change capital models and are requiring higher capital reserves. Contemporary risks are creating more volatility in the insurance marketplace. Higher volatility requires higher levels of capital kept in reserve to fund inevitable occasional large losses. A new generation of risk models is being developed to help insurers better calculate risks-especially catastrophic risk. The impact of new risk models on rating agency recommendations, insurers and the policy holders is discussed later in this essay.

Additionally, the results of the 2011 Risk Premium Project update found that behavioral insurance and new instruments of alternative risk transfer are popular fields of research in nonlife insurance. Capital allocation and enterprise risk management are also very important research topics. Furthermore, the financial crisis has stimulated new work on corporate governance and insurance (Eling, 2013).


Determining Premiums

A large part of success for insurance companies remaining solvent and making a profit can be attributed to calculating the correct premium for insurance coverage. As one might imagine, this is one of the most difficult undertakings for insurance carriers. Insurance companies need to charge enough for premiums to cover not only their claims losses, but also operation expenses and overhead. At the same time, insurers are facing stiff competition in many insurance lines and must keep premiums reasonable to keep customers from fleeing to lower priced competitors. Ratemaking is defined as the process of calculating a premium that is (All business, 2007):

  • Adequate: Enough to cover losses according to anticipated frequency and severity, thereby safeguarding against the possibility of the insurance company becoming insolvent;
  • Reasonable: The insurance company should not be earning excessive profit; and

• Not unfairly discriminatory or inequitable.

Rate Setting

Rate setting (historically) required basic information on a customer and then some previous history (experience). For example, an experienced driver has a driving record over a number of years that tracks accidents, but a new driver has no driving history to factor into rate setting. In such a case, computer databases make it easy to exclude certain criteria for certain rate predicting models and more accurately assign risk to given populations. Rate monitoring is the process of managing risk and rate structures for existing customers. Rate setting has two basic components: Pure premium and loss ratio (Using Data Mining for Rate Making in the Insurance Industry, 2003).

  • The pure premium is defined as the amount of total premiums of an insurance policy that is sufficient to offset all accident claim costs, also known as rock bottom of any premium structure. In this scenario, an insurance company could cover all claims from premiums, but would not make a profit or show a loss. Every premium dollar would be spent to cover claims with nothing left over for operating expenses.
  • Loss ratio is defined as the fraction of claim cost to premium. If the fraction for auto policies is 70% then this simply means that 70% of the premium collected needs to cover claim costs. The other 30% would go toward covering operation expenses or be recorded as profit. Lowering cost ratios is the major goal for insurance companies and it can be done in one of two ways: Premiums can be increased to cover claims; policy holders (customers) can be adjusted to get rid of higher risk customers-thereby lowering the number of potential claimants.


Another insurance term related to rate making is...

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