What Is a Standalone Risk?

From a macro perspective, the risk structure refers to the proportion of various types of insurance in the overall business of an insurance company. If the premium rate of the insurance type with a low compensation rate and good efficiency accounts for a large share, the company's risk structure is good, otherwise it is poor; From a micro perspective, the risk structure refers to the business of a specific type of insurance. If an insurance company looks at different insurance ranges from different coverage ranges, the premiums of the business with low compensation rates and good returns account for a large proportion of the insurance business. The risk structure is good and vice versa.

Risk structure

Right!

From a macro perspective, the risk structure refers to the proportion of various types of insurance in the overall business of an insurance company. If the premium rate of the insurance type with a low compensation rate and good efficiency accounts for a large share, the company's risk structure is good, otherwise it is poor; From a micro perspective, the risk structure refers to the business of a specific type of insurance. If an insurance company looks at different insurance ranges from different coverage ranges, the premiums of the business with low compensation rates and good returns account for a large proportion of the insurance business. The risk structure is good and vice versa.

There are two main types of risk structure: the interrelationship between risks: independent and dependent. When multiple risks are involved in insurance, they are often assumed to be independent of each other. For example, the Panjer recursion and DePeril recursion that determine the distribution of the Prime Minister's compensation in the aggregate risk model are based on the assumption of independence between individual risks, as in life insurance. The multiple life model and traditional actuarial mathematics textbooks assume that the remaining life of the insured involved are independent of each other. The independence assumption can bring great convenience. Because of this assumption, the law of large numbers and the central limit theorem have the premise of application. As a result, insurance companies can effectively manage risks through risk sets. Another advantage of the independence assumption is that as long as the statistical data (marginal distribution) of individual risks is given, the statistical distribution of the combined risk statistics can be easily obtained, which brings a great deal of mathematical processing in actual work. Convenience. However, in many insurance problems in reality, there is still a strong interdependence between risks, and it is not very clear to ignore this correlation. Here is an example of this: ^[1]

The simplest classical risk model has the following characteristics: ^[1]

Based on the classical risk model, many scholars have made a series of promotion consistent with the operating realities of insurance companies. Common promotion types are:

the first sort:

The claim arrival process includes the Guangli update process, the generalized compound Poisson process, the Cox process, the Gamma process, and the inverse Gaussian process. Using this model, you can take into account the fact that the strength of the claims counting process caused by seasonal or political factors is not constant.

The second category:

The premium arrival process is extended to Poisson process, Cox process, update process, etc. At the same time, the premium income rate is a constant, and Li is a random variable that is closer to the actual situation.

Third category:

Introduce the residual rate and investment factors, consider the interference of the diffusion process and the surplus process, or consider the payment of dividends, so that the risk model is closer to the actual operation of the insurance company.

Fourth category:

Various risk models of continuous-time situations are extended to discrete-time situations in parallel.

Fifth category:

That is, there is a certain relationship between various risks. The reality is that the insurer has data about a single risk, that is, information about marginal distribution, but no data about the information about risk, that is, information about joint distribution. This makes the mathematical treatment of dependent risks less regular To follow.