1 Glossary
Chapter Preview. Loss Data Analytics contains specific insurance and probability terms which are important to understand the concepts in the book. This glossary can serve as a quick reference when the reader needs to recall a term’s definition or location. We also include instructions if the reader wishes to suggest improvements to current definitions.
1.1 Making Changes to Terms and Definitions
When using the glossary, we encourage the reader to provide feedback regarding the terms and their definitions. For example, if the reader feels that there is a better definition for a particular term, the following instructions outline how the reader can suggest improvements.
- First, open up the issues tab on our repository on GitHub here.
- Click on “create an issue”.
- Indicate which chapters you want to make changes to in the title.
- Specify the terms and definitions you wish to change, add or remove.
- Click “Submit new issue”.
1.2 Terms and Definitions by Chapter
Here is a list of important terms and their definitions listed according to the chapters in which they are found.
1.2.1 Chapter 1 Introduction to Loss Data Analytics
| Term | Definition |
|---|---|
| loss adjustment expenses | Loss adjustment expenses are costs to the insurer that are directly attributable to settling a claims. For example, the cost of an adjuster is someone who assess the claim cost or a lawyer who becomes involve in settling an insurer’s legal obligation on a claim |
| unallocated loss adjustment expenses | Unallocated loss adjustment expenses are costs that can only be indirectly attributed to claim settlement; for example, the cost of an office to support claims staff |
| allocated loss adjustment expenses | Allocated loss adjustment expenses, sometimes known by the acronym ALEA, are costs that can be directly attributed to settling a claim; for example, the cost of an adjuster |
| indemnification | Indemnification is the compensation provided by the insurer. |
| insurance claim | An insurance claim is the compensation provided by the insurer for incurred hurt, loss, or damage that is covered by the policy. |
| loss amount | The loss amount is the size of the loss incurred by the policyholder for incurred hurt, loss, or damage that is covered by the policy. |
| analytics | Analytics is the process of using data to make decisions. |
| renters insurance | Renters insurance is an insurance policy that covers the contents of an apartment or house that you are renting. |
| homeowners insurance | Homeowners insurance is an insurance policy that covers the contents and property of a building that is owned by you or a friend. |
| automobile insurance | An insurance policy that covers damage to your vehicle, damage to other vehicles in the accident, as well as medical expenses of those injured in the accident. |
| property insurance | Property insurance is a policy that protects the insured against loss or damage to real or personal property. The cause of loss might be fire, lightening, business interruption, loss of rents, glass breakage, tornado, windstorm, hail, water damage, explosion, riot, civil commotion, rain, or damage from aircraft or vehicles. |
| nonlife insurance | Nonlife insurance is any type of insurance where payments are not based on the death (or survivorship) of a named insured. Examples include automobile, homeowners, and so on. Also known as property and casualty or general insurance. |
| casualty insurance | Causalty insurance is a form of liability insurance providing coverage for negligent acts and omissions. Examples include workers compensation, errors and omissions, fidelity, crime, glass, boiler, and various malpractice coverages. |
| valuation date | A valuation date is the date at which a company summarizes its financial position, typically quarterly or annually. |
| underwriting | Underwriting is the process where the company makes a decision as to whether or not to take on a risk. |
| ratemaking | |
| reinsurer | A reinsurer is an insurance company that offers insurance to an insurer. |
| loss reserve | A loss reserve is an estimate of liability indicating the amount the insurer expects to pay for claims that have not yet been realized. This includes losses incurred but not yet reported (IBNR) and those claims that have been reported claims that haven’t been paid (known by the acronym RBNS for reported but not settled). |
| technical provisions | Technical provisions is another name for loss reserves. |
| experience rating | |
| merit rating | |
| risk classification | Risk classification is the process of grouping policyholders into categories, or classes, where each insured in the class has a risk profile that is similar to others in the class. |
| cream skimming | |
| claims triage | |
| pure premium | Pure premium is the total severity divided by the number of claims. It does not include insurance company expenses, premium taxes, contingencies, nor an allowance for profits. Also called loss costs. Some definitions include allocated loss adjustment expenses (ALAE). |
| loss cost | Loss cost is the total severity divided by the number of claims. It does not include insurance company expenses, premium taxes, contingencies, nor an allowance for profits. Also called pure premium. Some definitions include allocated loss adjustment expenses (ALAE). |
| rating variables | |
| coinsurance | Coinsurance is an arrangement whereby the insured and insurer share the covered losses. Typically, a coinsurance parameter specified means that both parties receive a proportional share, e.g., 50%, of the loss. |
| deductible | A deductible is a parameter specified in the contract. Typically, losses below the deductible are paid by the policyholder whereas losses in excess of the deductible are the insurer’s responsibility (subject to policy limits and coninsurance). |
| policy limit | A policy limit is the maximum value covered by a policy. |
| personal lines | |
| dividend | A dividend is the refund of a portion of the premium paid by the insured from insurer surplus. |
| bonus | |
| retrospective premiums | The process of determining the cost of an insurance policy based on the actual loss experience determined as an adjustment to the initial premium payment. |
| prospective premiums | |
| claims adjustment | Claims adjustment is the process of determining coverage, legal liability, and settling claims. |
| Commercial line | Commercial line is insurance purchased by commercial ventures (businesses) |
| line of business | A line of business is a classification of business written by insurers. |
| claims leakage | Claims leakage respresents money lost through claims management inefficiencies. |
| fraud detection | |
| case reserve | A case reserve is an estimate of the insurer’s future liability made by the claims adjuster. |
| adjuster | An adjuster is a person who investigates claims and recommends settlement options based on estimates of damage and insurance policies held. |
| life Insurance | Life insurance is a contract where the insurer promises to pay upon the death of an insured person. The person being paid is the beneficiary. |
| capital allocation |
1.2.2 Chapter 2 Frequency Modeling
| Term | Definition |
|---|---|
| aggregate claims | The sum of all claims observed in a period of time |
| Bernoulli distribution | A special case of the binomial distribution where the number of trials is equal to 1, leading to only 2 potential outcomes: success or failure |
| Binomial distribution | A Frequency distribution of the possible nuber of successful outcomes in a given number of trials in each of which there is the same probability of success. |
| Distribution function F(x) | A Function that gives the probability that a discrete random variable is equal to or less than some value. |
| Frequency | The rate at which something occurs or is repeated over a particular period of time or in a given sample. |
| Gamma Distribution | A two parameter family of continous probability distributions that is defined by a shape and scale parameter. |
| Maximum Liklihood Estimator | The maximum likelihood estimator (mle) for θ is any maximizer of the likelihood; in a sense the mle chooses the parameter value that best explains the observed observations |
| Mixture | A probabilistic combination of two or more probability distributions |
| Moment generating function | A real function whose derivatives at zero are equal to the moments of the random variable. |
| Negative binomial | |
| Poisson | A discrete probability distribution that expresses the probability of a given number of events occuring in a fixed interval of time or space if these evetns occur with a known constant rate and independently of the time since the last event. |
| Probability generating function | A power series representation of the probability mass function of the random variable. |
| Probability mass function f(x) | A Function that gives the probability that a discrete random variable is exactly equal to some value. |
| Severity | The amount of damage that is (or that may be) inflicted by a loss or catastrophe. |
| Survival function S(x) | A function that gives the probability that an object of interest will survive beyond a specified time. |
| Zero Modifided Distribution | A modified member of the (a,b,0) class that has had its probability mass at 0 modified in some way. The rest of the probability masses are adjsuted to accomadate this modification. |
| Zero Truncated Distribution | A modified member of the (a,b,0) class that has a probability mass of 0 at 0. The rest of the probability masses are adjsuted to accomadate this modification. |
1.2.3 Chapter 5 Aggregate Loss Models
| Term | Definition |
|---|---|
| aggregate claims | The sum of all claims observed in a period of time |
| deductible | A deductible is a parameter specified in the contract. Typically, losses below the deductible are paid by the policyholder whereas losses in excess of the deductible are the insurer’s responsibility (subject to policy limits and coninsurance). |
| coinsurance | Coinsurance is an arrangement whereby the insured and insurer share the covered losses. Typically, a coinsurance parameter specified means that both parties receive a proportional share, e.g., 50%, of the loss. |
| inflation | Inflation is a sustained increase in the general price level of goods and services over a period of time. |
| policy limit | A policy limit is the maximum value covered by a policy. |
| line of business | A line of business is a classification of business written by insurers. |
| individual risk model | A modeling approach for aggregate losses in which the loss from each individual contract is considered. |
| collective risk model | A modeling approach for aggregate losses in which the aggregate loss is represented in terms of a frequency distribution and a severity distribution. |
| coverage | Insurance coverage is the amount of risk or liability that is covered for an individual or entity by an insurance policy. |
| exposure | A measure of the rating units for which rates are applied to determine the premium. For example, exposures may be measured on a per unit basis (e.g. a family with auto insurance under one contract may have an exposure of 2 cars) or per $1,000 of value (e.g. homeowners insurance). |
| frequency distribution | The random number of claims that occur under the collective risk model. |
| severity distribution | The randomly distributed amount of each loss under the collective risk model. |
| term life insurance | A term life insurance policy is payable only if death of the insured occurs within a specified time, such as 5 or 10 years, or before a specified age. |
| pure endowment | A pure endowment is an insurance policy that is payable at the end of the policy period if the insured is still alive. If the insured has died, there is nothing paid in the form of benefits. |
| support (of a distribution) | The set of all outcomes for a random variable following some distribution. For example, exponentially distributed random variable X has support x>0. |
| central limit theorem | Given certain conditions, the arithmetic mean of a large number of replications of independent random variables, each with a finite mean and variance, will be approximately normally distributed, regardless of the underlying distribution. |
| convolution | The convolution of probability distributions is the distribution corresponding to the addition of independent random variables. |
| law of iterated expectations | A decomposition of the expected value of a random variable into conditional components. Specifically, for random variables X and Y, E(X) = E[E(X|Y)]. |
| law of total variance | A decomposition of the variance of a random variable into conditional components. Specifically, for random variables X and Y on the same probability space, Var(X) = E[Var(Y|X)] + Var[E(X|Y)]. |
| compound distribution | A random variable follows a compound distribution if it is parameterized and contains at least one parameter that is itself a random variable. For example, the Tweedie distribution is a compound distribution. |
| Tweedie distribution | A compound distribution that is a Poisson sum of Gamma random variables. Because it can accommodate a discrete probability mass at zero and a continuous positive component, it is suitable for modeling aggregate insurance claims. |
| shape parameter | A numerical parameter of a parametric distribution affecting the shape of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). |
| scale parameter | A numerical parameter of a parametric distribution that stretches/shrinks the distribution without changing its location or shape. The larger the scale parameter, the more spread out the distribution. The scale parameter is also the reciprocal of the rate parameter. For example, the normal distribution has scale parameter . |
| exponential dispersion model | A set of distributions that represents a generalisation of the natural exponential family and also plays an important role in generalized linear models. |
| generalized linear model | Commonly known by the acronym GLM. An extension of the linear regression model where the dependent variable is a member of the linear exponential family. GLM encompasses linear, binary, count, and long-tailed, regressions all as special cases. |
| exponential family | A family of parametric distributions that are practical for modeling the underlying response variable in generalized linear models. This family includes the normal, Bernoulli, Poisson, and Tweedie distributions as special cases, among many others. |
| Monte Carlo simulation | A computerized statistical model that simulates the effects of various types of uncertainty. |
| empirical distribution | The empirical distribution is a non-parametric estimate of the underlying distribution of a random variable. It directly uses the data observations to construct the distribution, with each observed data point in a size-n sample having probability 1/n. |
| convergence (almost surely) | A type of stochastic convergence for a sequence of random variables X_1,…, X_n that approaches some other distribution as n approaches . |
| ground-up loss | The total amount of loss sustained before policy adjustments are made (i.e. before deductions are applied for coinsurance, deductibles, and/or policy limits.) |
| per-loss basis | Due to policy modifications (e.g. deductibles), not all losses that occur result in payment. The per-loss basis considers every loss that occurs, as opposed to the per-payment basis which considers only the losses that result in some payment to the insured. |
| per-payment basis | Due to policy modifications (e.g. deductibles), not all losses that occur result in payment. The per-loss basis considers every loss that occurs, as opposed to the per-payment basis which considers only the losses that result in some payment to the insured. |
| memoryless | The memoryless property means that a given probability distribution is independent of its history and what has already elapsed. Specifically, random variable X is memoryless if Pr(X > s+t | X >= s) = Pr(X > t). Note that it does not mean X > s+t and X >= s are independent events. |
1.3 Terms and Chapter First Defined
Certain terms are defined multiple times throughout the book, so this list can help the reader refer to the chapter in which a term is first used and defined. The terms listed here are sorted in alphabetical order.
| Term | Chapter first defined |
|---|---|
| adjuster | 1 |
| aggregate claims | 2 |
| allocated loss adjustment expenses | 1 |
| analytics | 1 |
| automobile insurance | 1 |
| Bernoulli distribution | 2 |
| Binomial distribution | 2 |
| bonus | 1 |
| capital allocation | NA |
| case reserve | 1 |
| casualty insurance | 1 |
| central limit theorem | 5 |
| claims adjustment | 1 |
| claims leakage | 1 |
| claims triage | 1 |
| coinsurance | 1 |
| collective risk model | 5 |
| Commercial line | 1 |
| compound distribution | 5 |
| convergence (almost surely) | 5 |
| convolution | 5 |
| coverage | 5 |
| cream skimming | 1 |
| deductible | 1 |
| Distribution function F(x) | 2 |
| dividend | 1 |
| empirical distribution | 5 |
| experience rating | 1 |
| exponential dispersion model | 5 |
| exponential family | 5 |
| exposure | 5 |
| fraud detection | 1 |
| Frequency | 2 |
| frequency distribution | 5 |
| Gamma Distribution | 2 |
| generalized linear model | 5 |
| ground-up loss | 5 |
| homeowners insurance | 1 |
| indemnification | 1 |
| individual risk model | 5 |
| inflation | 5 |
| insurance claim | 1 |
| law of iterated expectations | 5 |
| law of total variance | 5 |
| life Insurance | NA |
| line of business | 1 |
| loss adjustment expenses | 1 |
| loss amount | NA |
| loss cost | 1 |
| loss reserve | 1 |
| Maximum Liklihood Estimator | 2 |
| memoryless | 5 |
| merit rating | 1 |
| Mixture | 2 |
| Moment generating function | 2 |
| Monte Carlo simulation | 5 |
| Negative binomial | 2 |
| nonlife insurance | 1 |
| per-loss basis | 5 |
| per-payment basis | 5 |
| personal lines | 1 |
| Poisson | 2 |
| policy limit | 1 |
| Probability generating function | 2 |
| Probability mass function f(x) | 2 |
| property insurance | 1 |
| prospective premiums | 1 |
| pure endowment | 5 |
| pure premium | 1 |
| ratemaking | 1 |
| rating variables | 1 |
| reinsurer | 1 |
| renters insurance | 1 |
| retrospective premiums | 1 |
| risk classification | 1 |
| scale parameter | 5 |
| Severity | 2 |
| severity distribution | 5 |
| shape parameter | 5 |
| support (of a distribution) | 5 |
| Survival function S(x) | 2 |
| technical provisions | 1 |
| term life insurance | 5 |
| Tweedie distribution | 5 |
| unallocated loss adjustment expenses | 1 |
| underwriting | 1 |
| valuation date | 1 |
| Zero Modifided Distribution | 2 |
| Zero Truncated Distribution | 2 |