This text will focus on short-term insurance contracts. By “short-term,” we mean contracts where the insurance coverage is typically provided for six months or a year. If you are new to insurance, then it is probably easiest to think about an insurance policy that covers the contents of an apartment or house that you are renting (known as renters insurance) or the contents and property of a building that is owned by you or a friend (known as homeowners insurance). Another easy example is automobile insurance. In the event of an accident, this policy may cover damage to your vehicle, damage to other vehicles in the accident, as well as medical expenses of those injured in the accident.
In the US, policies such as renters and homeowners are known as “property” insurance whereas a policy such as auto that covers medical damages to people is known as “casualty” insurance. In the rest of the world, these are both known as “nonlife” or “general” insurance, to distinguish them from life insurance.
Both life and nonlife insurances are important. To illustrate, IAA (2015) estimates that direct insurance premiums in the world for 2013 was 2,608,091 for life and 2,032,850 for nonlife; these figures are in millions of US dollars. As noted earlier, the total represents 6.3% of the world GDP. Put another way, life accounts for 56.2% of insurance premiums and 3.5% of world GDP, nonlife accounts for 43.8% of insurance premiums and 2.7% of world GDP. Both life and nonlife represent important economic activities and are worthy of study in their own right.
Yet, life insurance considerations differ from nonlife. In life insurance, the default is to have a multi-year contract. For example, if a person 25 years old purchases a whole life policy that pays upon death of the insured and that person does not die until age 100, then the contract is in force for 75 years. We think of this as a long-term contract.
Further, in life insurance, the benefit amount is often stipulated in the contract provisions. In contrast, most short-term contracts provide for reimbursement of insured losses which are unknown before the accident. (Of course, there are usually limits placed on the reimbursement amounts.) In a multi-year life insurance contract, the time value of money plays a prominent role. In contrast, in a short-term nonlife contract, the random amount of reimbursement takes priority.
In both life and nonlife insurances, the frequency of claims is very important. For many life insurance contracts, the insured event (such as death) happens only once. In contrast, for nonlife insurances such as automobile, it is common for individuals (especially young male drivers) to get into more than one accident during a year. So, our models need to reflect this observation; we will introduce different frequency models than you may have seen when studying life insurance.
For short-term insurance, the framework of the probabilistic model is straightforward. We think of a one-period model (the period length, e.g., six months, will be specified in the situation).
- At the beginning of the period, the insured pays the insurer a known premium that is agreed upon by both parties to the contract.
- At the end of the period, the insurer reimburses the insured for a (possibly multivariate) random loss that we will denote as “y“.
This framework will be developed as we proceed but we first focus on integrating this framework with concerns about how the data may arise and what we can accomplish with this framework.