The Increased limit factors or ILF reference curves are multiplicative factors that are applied to premiums for “basic” limits of coverage to determine premiums for higher limits of coverage. It is used as a basis for the method of liability rating. Furthermore, It helps in determining how the expected loss increased by increasing the limit purchased and also helps in determining the cost of reinsuring a specific layer of reinsurance.

The liability and property are common terms used in pricing in general insurance. The main difference between the two is in terms of its construction of reference curves as they have different processes that are followed. Liability is known as having no upper limit to the size of the loss such as the sum insured or the maximum possible loss for the property. In liability, it is usually purchased up to a given limit, however, this limit does not provide in itself sufficient information on the potential loss severity.

Both the severity curves and the increased limit factor curves are common terms in exposure rating for the insurance. The relationship between the two is that there is a one-to-one correspondence between the increased limit factor curves and severity curves. Given the cumulative distribution function of a severity curve, we can determine the increased limit factor using certain equations.

The main application of the increased limit factors curves is in the context of excess-of-loss rating in reinsurance. The fact that the increased limit factors curves are only used to help determine the relativity between the expected losses at two different limits but are mute about the absolute expected losses, which is the reason why we need to assume that we have the expected losses capped at a limit to start with.

There are several ways in dealing with the issue of the derivation of increased limit factors and the ISO Methodology is one of the most commonly used methods in dealing with these issues. It is important for the derivation of increased limit factor curves because it shows how increased limit factors curves are derived in actual practice and also shows an example of how a severity model distribution can be built based only on the closed claims.

Tort law is the legal framework used for professional indemnity policies because it is for all liability insurance. However, these policies include dealing with negligent advice given by professional people, so, therefore, elucidating the impression that it applies to all professionals, whether they are medical doctors, actuaries, engineers, or lawyers.

Weather derivatives are a risk management tool that is used to allow the organization to protect themselves against the financial consequences of the vagaries of weather. It is index-based instruments that usually use observed weather data at a weather station to create an index on which a payout can be based. This index could be total rainfall over a relevant period—which may be of relevance for a hydro-generation business—or the number where the minimum temperature falls below zero which might be relevant for a farmer protecting against frost damage.

The weather derivative is used for the context of shifting the attention from the loss of profits to the weather itself. It is because the payout is not related to the actual loss of profits of the organization but it is simply triggered by the value of an index, which is based on the objectives, uncontroversial weather data obtained by a weather station whose independence is recognized by both seller and buyer.

According to Palmer in 2006, there are two main assumptions behind the increased limit factor reference curves which can be enumerated as the independence of the limit purchased of the ground-up loss frequency and that there is also independence in the number of losses and of the limit purchased of the ground-up severity. These two assumptions mentioned are quite reasonable although it is not questionable.

As the increased limit factors are normally derived through the consideration of large amounts of market losses and building a severity distribution, Palmer found several issues that may arise in the derivation of increased limit factors which are the same issues as when trying to build a severity curve based on loss data. These issues include the fact that there may be some losses that are censored because of the policy limits, some losses may be the net of a deductible, there are uncertainties as the losses are required to be revalued, and lastly, there is going to be IBNER as many claims are still open.

The ISO Methodology used for dealing with the issues of the derivation of the increased limit factor curves can be outlined in eight processes. The first thing that should be considered is that all closed losses information on the time at which each intermediate payment was made is called input. The outline can be enumerated as First, the revaluation of all closed claims losses to the midterm of the policy. Second, the subdivision of the loss data according to the payment lag. third, The calculation of the empirical distribution of closed claims for each payment lag. Fourth, the estimation of the percentage of losses that are settled for different payment lags, etc.

Other issues may arise in calculating the liability rating using the increased limit factors curves such as the index clause, discounting, dealing with expenses, and per claim versus per occurrence. The index clause has an effect that can be roughly taken into account by considering the weighted payment time or the mean settlement time. Discounting for investment can also be done in experience rating. Dealing with expenses involved in general both allocated and unallocated expenses. ILFs can be provided on a per claim basis or a per-occurrence basis.

It is common knowledge that the increased limit factor curves are used for the calculation of the liability rating. The examples of this can be enumerated as follows; ISO Curves which provides ILF curves for a variety of casualty businesses, National Council on Compensation Insurance Curves which focuses on the worker’s compensation business, and Riebesell Curves which is commonly used in European casualty treaty business.

The policies included in the professional indemnity cover are characterized as a claims-made basis, retroactive date, and reinstatements. The policies for professional indemnity are known to be commonly sold on a claims-made basis wherein the policy would pay for the losses that are covered for a certain period. It could also be a mature policy that may be applied to all reported claims regardless of the date of occurrence and it also often includes a provision for reinstatements like many reinsurance policies do.

Reinstatements have two types that are available for the professional indemnity policies which are direct reinstatements and round-the-clock reinstatements which is the exotic type of structure. Direct reinstatements are commonly used wherein once a layer of reinsurance is exhausted, it is already reinstated as often as specified in the contract. Round-the-clock reinstatements have a dependency on the various layers of insurance created.

In insurance, several methods are proposed for the valuation of weather derivatives. Two methods are commonly used for the valuation and it consists of the option pricing techniques and the actuarial method. Either of the methods can be used for the valuation of the weather derivatives. However, the actuarial method is considered to be the most commonly used approach to valuation.

Credit risk refers to the probability of loss due to a borrower’s failure to make payments on any type of debt. When there is a possibility that the borrower fails to pay any type of debt, the business will lose some of its revenue. The major benefit of integrated, quantitative credit risk management is to reduce revenue losses. Monitoring your credit risk allows your executive management team to understand which potential clients may come at too high a risk and above your pre-identified risk tolerance.

The hazard module only focuses on the characteristics of the catastrophic event but what the companies want to know is the amount of possible damage the catastrophic event could cause to the company’s property, so the vulnerability module is very important for the companies as it translate the hazard characteristics into the expected physical damage after considering the characteristics of the properties in the portfolio.

Actuaries are not the ones responsible for doing the catastrophe modeling but they need to know the catastrophe models for the consideration of catastrophes to inform their activity in pricing, reserving, and capital modeling. It is needed to be known for the actuaries as the catastrophic events could have a big impact on pricing insurance.

The experience-based calculation of the risk-premium for an insurance policy can be affected by several sources of uncertainties wherein the most obvious uncertainty is the limited size of the historical database of losses of the client. The analysts could use average, or typical information from the market for replacement of the client risk premium. However, the use of these replacements could be a problem as the market experience is not ensured to be relevant to a particular client.

Credibility theory is a form of statistical inference used to forecast the uncertainty of a future event which is developed by Thomas Bayes. It may be used when you have multiple estimates of a future event, and you would like to combine these estimates in such a way to get a more accurate and relevant estimate. This is the most standard way of combining the client and market information.

Risk factors are the characteristics of the policyholder, which can be an individual or a company, that makes the policyholder more or less risky that the policy is more or less expensive to cover. This definition of risk factors already includes everything, whether it is measurable or not.

The option pricing method is one of the methods used for the valuation of weather derivatives. However, several issues and difficulties might arise with the use of this method, so several individuals or professionals proposed the possible workarounds of the issues. One of the proposals is the German’s proposal of the use of an energy contract instead of the meteorological index as the underlying variable and the other one is the proposal about the use of correlated weather futures contracts instead of meteorological index.

Finding the index is the first phase of the actuarial valuation method. In understanding this phase, it is important to know the detailed steps or processes that should be followed to get a relevant result. These steps can be enumerated as follows: First, input the revenue-related data. Second, detrending the revenue-related data. Third, finding relevant weather data. Fourth, finding the index that best matches the profit data and lastly, the validation of the index.

Modeling the payout is the second phase of the actuarial valuation method. This phase consists of four detailed steps that are enumerated as detrending the weather variables, modeling the index, estimating the payout, and determining the premium, respectively.

The hazard module is one of the three components that describe a catastrophe model. This component can do two different things in calculation related to catastrophic events. One of the things that it can do is that it generates a set of potentially catastrophic events. It can also be used for assessing the level of physical hazards for each event.

The catastrophe model is considered to be a typical sophisticated piece of software that is produced by a specialist company. Three components are made up to describe a catastrophe model. First, the hazard module that models the peril. Second, a vulnerability module that estimates the likely damage or injury that is probable to suffer because of the hazard. Third, a financial module which estimates the financial loss that would occur due to these damages.

Depending on the ‘events loss table’ or the ELT, several outputs of the catastrophe model can be produced. Five different outputs can be found on the event loss table of a catastrophe model and it can be enumerated as the following: the occurrence of exceedance probability, the aggregate exceedance probability, return period, average annual loss, and lastly, the standard deviation.

The commonly used approach used is the framework of uncertainty-based credibility as a relatively straightforward way of illustrating the concept of credibility. However, several different approaches to credibility have already been developed through the years to achieve the trade-off between accuracy and relevance in their different way. These approaches include classical credibility, Bayesian credibility, and Bühlmann credibility.

The effect of a properly performed rating factor selection in the non-life insurance industry has a very big impact on the competitive position of the company. A company that can analyze the claims data and extracts a large number of rating factors has a great competitive advantage over its competitors.