Читать книгу Pricing Insurance Risk - Stephen J. Mildenhall - Страница 37

The International Organization for Standardization (ISO) Guide 73:2009 defines risk to be the effect of uncertainty on objectives, where an effect is a deviation from what is expected. Risk is caused by events which have consequences. The pivotal word in the definition is uncertainty, which ISO defines as “the state, even partial, of deficiency of information related to, understanding or knowledge of, an event, its consequence, or likelihood.”

We use the ISO definition of risk. Insurers also use the risk to refer to the peril (earthquake, fire, flood, etc.) that may cause a loss and use a risk as a synonym for an account, case, insured, contract or policy, or for the subject of a policy.

There is a fundamental distinction between speculative risk and pure risk. A pure risk or insurance risk has a potential bad outcome but no good outcomes. It is a possible loss with no chance of gain. Insurance policies are designed to put the insured, at best, in the same position they would have been without a loss (in order to avoid morale hazard). A speculative risk or asset risk has both good and bad outcomes; it can be a loss or a gain. Reframing can convert a pure risk into a speculative one. The loss on an insurance policy is a pure risk. But the net position, premium less loss and expense, is a speculative risk.

An uncertain outcome that involves a choice is called a prospect. A prospect is relative to a reference point. The uncertainty in your bonus is relative to what you expect, not zero. Business is evaluated relative to plan, not insolvency. This can make the distinction between pure and speculative risks a matter of definition; an insurer can focus on the policy loss payments (pure risk) or on the net position of premium less losses (speculative risk). The existence of different reference points can also lead to framing bias problems, described in Kahneman (2011).

A prospect with outcomes denominated in a monetary unit is called a financial risk. An insurance loss, the future value of a stock or bond, and the present value of future lifetime earnings are examples of financial risks.

A financial risk can have timing uncertainty, amount uncertainty, or both. It can involve:

 Payment of a known amount at a random time, e.g. benefit payment on a whole or term life insurance policy.

 Payment of a random amount at a known time, e.g. payment on a pure endowment policy, which pays if the insured survives to a certain age or payment of a year-end employee bonus if the employer profit target is met.

 Payment of a random amount at a random future time, e.g. loss payment on a typical property-casualty insurance policy.

Insurance contracts can reduce timing or amount uncertainty, or both, for example by specifying payment dates or applying limits and deductibles to loss amounts. Accounting rules often require that reinsurance contracts transfer both timing and amount risk.

Risk is time separable if a measure of the magnitude of the risk of an amount at a future time can be expressed as the product of (1) the magnitude of the risk of the amount if immediately due, times (2) a discount factor. In this book we will assume risk is time separable. Under time separability a risk measure becomes a measure of amount risk. (Timing risk and discounting are discussed in Chapter 8.)