In a portfolio of general insurance risks, such as a portfolio of motor insurance, two obvious quantities of interest can be found which can be enumerated as the following: first quantity is the number of claims that arrive in a fixed period, and the second quantity is the sizes of the number of claims. These quantities are represented as random variables with appropriate probability distributions.

Many probability distributions are available as models for both claim numbers and claim sizes in general insurance. For claim numbers, the suitable models are called “counting distributions” which is described as the distributions of discrete random variables that can assume some or all of the values in N= {0, 1, 2,….}

For the actuaries to learn how to do pricing, the need to have a good working knowledge of the products that they will have to price. It is important for the actuaries to first learn about the products for them to properly come up with a suitable price for the product.

There are several aspects to the knowledge of the products that will be priced: the first aspect is the knowledge of the risk underlying a product, the second aspect is the knowledge of the technicalities of the policy, and the last aspect, which quite wide, is the environment your business operates in.

Many probability distributions are available as models for both claim numbers and claim sizes in general insurance. For the claim sizes, the suitable and widely used models are called distributions of continuous random variables that only assume positive values and it has “fat tails” or “heavy tails”, these distributions allow occasional occurrences of a large number of values.

The knowledge of the risk underlying a product is one of the several aspects of the knowledge of the products that will be priced. It focuses on knowing the risks that could arise from the product and knowing its competitive value by comparing its risks from other products by considering different risk factors such as flood, fire, theft, and earthquake.

A fat-tailed or heavy-tailed distribution exhibits a large kurtosis and skewness in the frequency of distribution which implies a lack of symmetry of the distribution wherein the tail decays like a power-law distribution. It is a distribution that allows the occurrences of a large number of values.

The most widely used model for the process which gives rise to claims in the business in general insurance portfolio is called a “Poisson Process”. The claims in the Poisson process arise “at random”, one after another through time and at a constant intensity.

The Prudential Regulation Authority classification scheme was developed by the Financial Services Authority (FSA) which was the former regulator in the insurance business in the United Kingdom. Now, it has been split into two different authorities: the FCA and the Prudential Regulation Authority (PRA) which the latter authority now has control of the classification scheme.

According to the classification method of products by category cover, insurance products can be classified into four broad categories: liability, property, financial loss, and fixed benefits. The categories depend on the type of losses that are indemnified and the type of compensation itself.

At a very high level in the pricing process, it consists of several steps: First is familiarizing the risk with the insured business. Then, with the given information on claims, exposure, and cover, the cost of taking on the risk would be estimated. The fourth step is taking into account the related cost of running the business and investment income. The fifth step is the addition of allowance for profit, thus obtaining the technical premium, and lastly, based on the technical premium and commercial considerations, the actual premium to be charged would be determined.

Insurance categorized as products by type of customers has three different classifications which can be enumerated as personal lines which is insurance that focuses on the individuals, commercial lines which is insurance that is for companies, and lastly, reinsurance which is for the insurers. Personal lines and commercial lines business are together called “primary business”, in the sense that they are non-reinsurance.

The absence of individual loss information makes it difficult to price insurance policies with non-proportional elements because the calculations are limited to the aggregate information which is the total claims reported in each year, ignoring the information of the individual claims that make up the aggregates. For instance, If we have only aggregate claims information, there are certain things that we cannot do, such as analyzing the effect of changing the retention threshold.

The principle of Indemnity is one of the leading principles used in general insurance. It is relatively straightforward when applied to property insurance in which the compensation must be provided for the lost goods to be replaced or put you back in the financial position before losing the goods.

Despite the limitation of only focusing on the aggregate information of the claims, there are good reasons why it made sense to dwell on it. There are two reasons why it is being used; The first reason is that it is actually the basis on which many underwriters and risk managers look at risk and the second reason is that this approach provides a broad feel to the risk managers of what the risk is like and a sense check on any subsequent actuarial analysis.

Adjustments are allowed in the process of calculating the past claims experience as there are circumstances that would require the actuaries to adjust due to the changes that occurred in the process. Adjustments are needed if there are significant changes of cover that are made that could result in not including previous claims that were previously covered. Adjustments would also be needed if there are changes in the legislation aspect and when unusual experiences should be corrected for different weather conditions, currency effects, and for anything that will be appropriate.

The formula of total expected ceded losses is multiplying the percentage of the insurance to the total losses so to get the total expected ceded loss of ABC corporation, we will just simply multiply 80% to the total of losses, $349,900, which would result to $279,920 total expected ceded losses. The limitation of ₱100,000 on each loss and in aggregate for each year would be ignored.

The expected ceded losses of 279,920 that are computed by multiplying total losses to the percentage of available insurance will be divided by 80% to get the total expected ceded losses plus expenses of $349,900. The 20% premium for covering the expenses would now be written-off.

For ABC Corporation to forecast how much they need to pay for the employer’s liability for 4 years’ time, the target amount of payment, $529,000, will be divided by the percentage of return per annum plus 1 raised to the fourth power which equals to $435,210. If $435,210 of the premium would be charged today, the ABC corporation will have to pay $529,000 for claims and expenses in 4 years’ time.

Exposure measures are the measures that are known to be roughly proportional to the overall risk, which in turn translates into the total expected losses. Wageroll is one of the often used exposure measures for burning cost analysis in employers’ liability. Also one of the exposure measures used is the number of employees which can also be called “employee-years” as it gives appropriate weights to part-timers and employees joining/leaving during the year.

From the point of view of pricing, there are two characteristics of property policies. It is characterized by short-tail claims which can be described as losses that are usually immediately discovered and it is also characterized by a relatively low frequency of significant claims.

There are many questions that would arise in insurance but the main question that is often and the most important to be asked is what risks are we covering against? as there are numerous available risks that can be included in the insurance such as fire, flood, and theft insurance so it is important for the property insurance to have specified types of risks that would be included in the agreement.

All of the following examples of property policies are one of the large numbers of covers that fall under the heading of property insurance except the damage to third-party property as it is one of the examples of damages that liability insurance may cover.

In commercial lines, it is typically not an individual but a company or an organization. Despite the difference between the two as an entity, the need to protect its property and itself from the legal liability and financial losses are given importance. The main difference between the two is that the insurance needs of an organization are inevitably more complex than in individuals.

Normally, reinsurance is subdivided into treaty reinsurance which is described as an umbrella agreement between the insurer and reinsurer, and facultative reinsurance wherein each insurance contract is negotiated and reinsured on its own merit. Reinsurance can be further subdivided into proportional insurance wherein the cedes to the reinsurer in a predefined proportion of the claims and the premiums, and non-proportional insurance in which only insurance losses above a certain threshold are passed on the reinsurer.

There are seven fitted distributions that can be used as a method in calculating values in insurance which can be enumerated as exponential, gamma, lognormal, Pareto, Weibull, burr, and log gamma distributions. All of the seven fitted distributions can be presented in quantile-quantile plots for further visualizations of the data.

The value of the test statistics can be evaluated in either of the two ways. First, the value would be converted into a P-value which is a measure of the strength of the evidence against the hypothesis that the data do follow the fitted distribution so a small P-value would indicate that the data do not follow the fitted distributions. Second, the value would be compared with the values in published tables of the distribution function of the appropriate x squared distribution so if the value of the statistic is low, it can be concluded that the fitted distribution provides a good fit to the data.

Mixture distributions have many functions in general insurance. One of the functions of mixed distributions is that it enables us to include in models for claim amounts the variability amongst risks in a portfolio. It can also provide sources for further fat-tailed loss distributions and during the process of mixed distributions, other distributions that are already known will again come into the light and will be further explained by the mixed distributions.

There are many categories of tort law, but the most important for liability insurance is that of negligence which is an idea that someone who had a duty of care to others failed to do so. This category of tort was introduced to attempt the repackage of the evangelical principle ‘Thou shalt love thy neighbor as thyself’ into a form that the lawyers and judges could use.

The method of maximum likelihood is a widely used method for parameter estimation as the estimates that would result from this method are those values of the parameters which give the maximum value attainable by the likelihood function denoted by L.