A pool is an arrangement by which several individuals or companies decide to share premiums or losses in an agreed proportion while a self-retention group is an insurer that has been set up to insure the risks of its members. Based on the studies, the difference between pools and the self-retention group has no clear distinctions and it is considered that a self-retention group is a part of the pool arrangement with a company structure.

P & I Clubs are associations of ship-owners that provide cover for the marines, especially the marine liability. These associations were set up at a time when a cover for marine liability is rarely seen in the market so they decided to just provide it for themselves by mutual associations. They don’t only provide insurance for the marines, but they also provide technical assistance to ship-owners.

Brokers are intermediaries whose function is advising clients on the insurance purchase that they are considering to make so that it would be ensured that the buyer would get the best deal in the market, in terms of both cover and price. They are also the one who executes the transaction between the buyer and the insurer. They are required to act in the client’s best interest, not the insurer’s or theirs.

Independent financial advisors and consultancy firms function as an advisor on a range of financial decisions, ranging from mortgage to investment to audits to insurance purchase. Both have distinctions from professional brokers. In the case of consultancy firms, the difference is that a consultancy firm would only advise their clients but will not transact the business while professional brokers advise at the same time to transact the business of the client.

It is not a surprise that the largest insurance markets are located in the countries that have the largest economies which include the United States, Germany, Japan, United Kingdom, France, and other countries. There are also specific insurance markets that are considered important and one of these markets is the popular London market.

The steps of a slip system can be enumerated as: First, the broker would prepare a slip with the main features of the risk that includes a substantial amount of information as the term ‘slip’ suggests then the broker would show the slip to underwriters who will quote the premium. After the premium is quoted, the cedant would select a lead underwriter and a firm order price then that lead underwriter would accept a share of the risk and stamp and sign the slip. The step would go on until 100% of the order is reached or at the renewal date.

Nowadays, personal lines insurance is often purchased online with the use of an insurance aggregator. These works if the insurers agree to have their quotations appear on the aggregator’s website and there would be a fee that would be paid if a sale occurred. Normally, personal lines insurance would be placed through agents wherein you will go to the agent to explain your need and the insurance would be already arranged. It could also be through the brokers where the individual’s needs would be discussed and they will take a percentage of the premium from the insurance companies.

The existence of the underwriting cycle is a confirmation that ultimately the premium charged for a policy is a commercial decision and not a technical one so obviously, not all classes of business in insurance are equally affected by the cycle. For example, is a personal lines business, it is not that much affected by the cycle as it is subject to less violent swings.

The job of pricing actuaries would be much easier for the insurers if they could remain oblivious to everything except the portfolio of risks that they have to price. However, the price of the insurance and even the pure cost of risk is linked to the numerous factors that are out of the control of the individual or the company that wishes to transfer the risk and to the company that takes this risk.

Of all the factors that affect pricing, the regulatory environment is considered the most obvious as it imposes constraints on what products can be insured, how much capital must be held by insurers, and possibly how products should be priced.

In the legal environment, the claims and amounts are affected by legislation and court decisions. It could be ignored almost completely by actuaries by looking at past statistics to model the claims process in case of no changes in the legal environment. However, the legal environment constantly changes, so for example, a loss that occurred 10 years ago would warrant different payot where it occurs today, regardless of inflation.

The changes in the legal environment could either increase or decrease the frequency and severity of claims. It may increase the frequency and severity of claims by extending the scope of compensation or by introducing new counts of liability. Allowing the possibility of no-win, no-fee claims in the late 1990s became a reason for opening the floodgates to a large number of claims is an example of an increase while all of the other choices are an example of a decrease of frequency and severity of claims.

In terms of numerical approximations, it is relatively easier to work with Fourier transforms because of the wide availability of fast Fourier transform routines that can be used in the software packages. The fast Fourier transform algorithm takes as input a finite-dimensional array.

Compound distributions mostly arise from known distributions for the counting variable and the step variable. However, in practice, the theory would most likely produce an underlying distribution that is not commonly known to the use of statistical methods are required to make inferences about the underlying distributions and the resulting quantities of interest, from the available data.

As the other approximations have been studied for the individual risk model, it gives rise to the introduction of the popular Panjer recursion algorithm which is used for numerical evaluation of various types of compound distributions. With this, it became much easier to calculate the total claim amount for the collective risk model than for the individual risk model. This led to further study of the collective risk model approximations for the individual risk model.

There are several other premium calculation principles available that could be used as an alternative principle, in particular, one or two based on an adjustment to the distribution function of the risk which produces a weighted version of the original density function wherein the weight decreases as x increases, producing a density with fatter tails than it had originally.

Credibility theory provides a framework for setting premiums in general insurance. It produces an important illustration of experience rating, in which the premium is based on the information coming from the recent history of the risk and the possibility that of the other, comparable, risks with relevant information to add to the premium setting process.

The posterior distribution is the combination of the prior information and likelihood to produce an updated distribution and the density of the posterior distribution would be written. It provides a summary of the combined knowledge from the prior beliefs and the data expressed in the likelihood. It is where the Bayesian inference is based.

The Pricing actuaries should be knowledgeable about the current general economic conditions, especially in writing specific classes of business that depend on the economy. Specific methodologies are necessary to be developed for those classes of business that have such systematic dependence as those different classes of business have different policy structures.

Take note that currency movements may affect the performance of insurers writing policies in different territories. The given values are in British pounds and euro so to get the expected loss ratio, the values should be in the same currency so there will be conversion. The 250k euro would be converted to British pound so the converted value would be 312,500 British pounds. 500k British pound would be divided into the exchange rate of 1.25 British pound per one euro and then the result would be divided to 312,500 British pounds over 1.25 exchange rate which would result in a 160% loss ratio.

The underwriting cycle is the phenomenon that is ubiquitous across most classes of insurance. There are several reasons why there is a cycle in general insurance which includes: In case of a hard market, the insurers would gain incentives to enter the market or to move into a certain class of business, the increase of supply of insurance would result to the decrease of the price, In case of a soft market, it would occur if the price of the insurance would be not enough to provide an appropriate return on capital and lastly, the decrease of supply of insurance would result to the increase of price.

There are different possible ways in which the regulatory framework affects insurance in general. The list of possible ways includes product restrictions, premium restrictions, information restriction, and capital requirements. It is important to note that some of the following requirements such as premium restrictions and information restrictions will affect pricing directly. Some of the requirements, such as capital requirements, will affect the pricing directly while others, such as deposit requirements, are unlikely to have an effect in pricing in any significant way.

In the insurance business, the insurer is the one responsible for providing insurance cover against risks that are agreed upon. The insurer is the one who would offer to provide the policy with certain benefits under particular conditions and contracts that will be in the stated price which is called the premium.

Bayesian methodology lies within the general framework of decision theory wherein the consequences of actions or decisions are considered in the context of criteria based on the concept of a loss function. One of the well-known criteria is the minimax criterion, in which the action would be chosen for which the maximum possible loss that can be suffered as the result is minimized while a Bayes criterion is choosing an action for which the loss of Bayes would be minimized.

In a Bayesian credibility theory, a premium that would be set for the next years for a risk covered by the contract of general insurance by using the estimates of the parameter in a probability model. The estimate could be based on information from the two sources which includes the recent past data from the risk itself and using relevant information from the other sources.

The natural environment plays a major role in insurance, be it through normal weather events and seasonality or major catastrophes such as extreme weather events and geophysical events. Weather is mostly the source of many insurance claims, either directly, such as a hailstorm ruining a harvest which could cause a crop insurance claim, and indirectly, such as car accidents due to poor visibility and poor road conditions that mostly occur in the winter season.

Pricing in the corporate context is not an isolated activity in the company but has a relation to what other actuaries and other professional figures in the company do. The main functions of an insurer include planning function, underwriting function, claims function, actuarial: reserving, actuarial: capital modeling, finance, management information, investment function, reinsurance function, and other functions such as marketing function, sales function, and infrastructure functions.

Other functions of the insurer in the company include the marketing function which identifies successful insurance products and promotes them in the marketplace, the sales function, which coordinates the sales operations of the company, and infrastructures functions such as IT, HR, Legal, and Compliance which are all necessary for the functioning of the company. These other functions mostly have an indirect relationship with pricing actuaries.

Mostly, the relationships between the finance function and the pricing function are indirect, with some exceptions such as expense allocation. The premium charged for a policy contract normally includes an allowance for expenses which includes costs related to the claims handling process, the policy management process, and a contribution to the infrastructure expenses of the organization. The finance function would normally allocate capital expenses from the group down to portfolios then the underwriter and the pricing actuaries can now work out how to split them at the level of the individual contract.

Besides all information discussed, other things should also be known by the actuaries. It includes information about political risk, latent claims, medical risks, and scientific and technological advancements. It is information on the other factors that could also affect the pricing in insurance.