General insurance

## An Introduction

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Insurance companies satisfy much of society's demand for risk management. This is good for groups and individuals as it allows more risky ventures to be undertaken.

Examples of short term insurance companies are :

* United States:
* State Farm Group
* Allstate Insurance
* Berkshire Hathaway

* Japan
* Tokio Insurance
* Yasuda
* Mitsui

* Germany
* Allianz Vers
* AXA Colonia Vers
* HUK Coburg

* United Kingdom
* Royal and Sun Alliance
* Guardian Royal Exchange
* BUPA

* France
* AXA
* Groupama
* AGF

* Italy
* Generali
* Assitalia
* Sai

* Canada
* CGU Group Canada
* ING Canada
* Co-Operators Group

* Malawi
* General Alliance Insurance Limited

* Tanzania
* Star General Insurance (Tanzania) Limited

* Thailand
* The Viriyah Insurance

* Zambia
* General Alliance Insurance (Zambia) Ltd

Most insurers today are shareholder owned (proprietary) companies. There are still, however, many policyholder owned (mutual) insurance groups.

### The Balance sheet

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The financial position of an insurance group can be described using a balance sheet. Balance sheets show a listing of a business's (1) assets and (2) liabilities.

On the asset side, insurance companies hold various items, such as :

* equity (ownership in other companies)
* bonds (certificates entitling the company to interest and capital repayment from government or other companies)
* property (real estate)
* cash
* other assets (works of art etc.)

The policyholder liabilities (reserves) of a short term insurer's balance sheet typically consists of :

* liabilities with respect to past events / outstanding claims
* outstanding reported claims reserves
* reserves in respect of potential claims that have not yet been reported (IBNR)
* reserves in respect of claims that could potentially be re-opened
* reserves in respect of claims handling costs

* liabilities with respect to potential future events / unexpired risks
* reserves in respect of premium received but which is not yet earned
* reserves in respect of risk periods that have not yet elapsed

The liabilities can be shown as an aggregate amount for outstanding claims as well as an aggregate amount for unexpired risks.

In addition to the above , some (re)insurers also hold reserves with respect to potential catastrophes and so-called claims equalization reserves.

### Outstanding Claims

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Outstanding claims liabilities exist as a result of delays between the occurrence of the loss event and the reporting of the event (reporting delays => IBNR reserves) as well as delays between the reporting and settling of claims (settlement delays => outstanding case reserves). Premature closing of claims result in re-opened claims, and this results in reserves for future potential re-opened claims.

Reserves are typically larger for classes of insurance where delays between loss events and settlement are the longest (eg. Product Liability).

Estimates of claims reserves are made using two approaches :

* case reserves : estimating future payments in respect of individual (large) reported claims
* statistical reserves : using statistical methods to estimate ultimate claims (and therefore the amount of required reserves)

Case reserves are only made for reported claims. They are not made for unreported claims. Statistical methods are used to estimate the amount of 'incurred but not reported' (IBNR) claims.

Claims reserves are only estimates. As such, care must be taken to allow for the assumptions and uncertainty associated with the reserve estimates. Uncertainty is usually greater for 'longer tailed' classes of business (e.g. Product Liability).

### Unexpired Risks

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Unexpired risk reserve (URR) is a prospective assessment of the amount that needs to be set aside in order to provide for claims and costs that will result out of unexpired future periods of cover. This could be greater than the corresponding amount of premiums charged (UPR).

Unearned premium reserves (UPR) are premiums which have been set aside because the corresponding period of insurance cover has not yet elapsed. E.g. Premiums received in 2007 in respect of insurance cover in 2008 will not add to the 'earned premium' of the insurer in 2007, but will be set aside in a reserve (UPR).

AURR is the amount by which the URR exceeds the UPR (if any). If AURR > 0, it suggests that premium rates were originally set too low (at loss making levels).

### Shareholder capital

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Shareholder capital (aka free capital / free assets / solvency margin / shareholder funds / capital used ) is the amount by which assets exceed policyholder liabilities.

Higher levels of shareholder capital typically allows :

* a larger amount of business which the insurer can reasonably transact
* bigger risks can be underwritten
* more risk can be taken with asset investment (in pursuit of higher returns)
* less reinsurance protection is required

The main influences on the investment strategy of a short term insurer are :

* the nature, duration, level and currency of potential claims outgo
* the relative size of shareholders' capital
* relevant legistlation / regulation

A short term insurer's profit is the amount by which premiums exceed claims and cost outgo.

When calculating profit, one needs to use earned premium (as opposed to received), and incurred losses (as opposed to paid).

Incurred losses equal paid losses plus the change in reserves (claims reserves at yearend less claims reserves at the beginning of the year).

Underwriting profits equal earned premium less incurred claims less incurred costs.

### Cash flow

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A short term insurer's cash flow consists of :

Inflow :

* premiums
* investment income (dividends from shares / interest from bonds)
* capital inflow (from shareholders)
* reinsurance receipts (recoveries)

Outflow :

* claims
* costs
* investment made in shares / bonds
* distribution payments (dividends) to owners (shareholders) and creditors (bondholders) of the insurer
* tax to the government
* reinsurance payments (premiums)

### Reinsurance

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Reinsurance protects insurers against claims and losses from events which could otherwise threaten the continued existence of the insurance company.

## Premium rating

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Premiums are the amounts paid by policyholders to insurers for protection against unintentional and accidental losses. The starting point with premium calculation is normally the determination of expected claims outgo (aka the risk premium).

Experience rating is an approach adopted where the premium charges depends (at least in part) on the policyholder's past claims experience. It can be applied retrospectively (where premiums charged for past periods of cover are adjusted) or prospectively (where premiums are determined for future periods of cover). Experience rating can be applied with reference to either claims frequency or claims size.

### The risk premium

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The risk premium is the amount of premium needed to cover the expected claim amount of a policy. It is defined as :

Risk premium = expected number of claims x expected claim amount per claim

This can be expresed in terms of the insured value as follow :

Expected claims ratio = expected loss frequency per policy / average insured value per policy x expected loss size

For the purpose of analysis, data is typcally grouped into homogeneous groups.

In order to correctly price contracts, insurers require a sufficient amount of relevant, complete, and reliable data. Policy data as well as claims data is required as well as additional data to allow necessary adjustments and loadings to be made.

Internal data is often more appropriate than external data, although knowledge about market experience and competitors' premium rates is very important as well.

Proposed premium rates should allow for circumstances expected during the period of cover. Abnormal data features, changes in cover provided, and trends in claims size as well as claims frequency should be allowed for (adjustments made).

A so-called burning cost approach is often adopted whereby the actual cost of losses incurred during a previous period is expressed as an annual rate per unit of insured value (exposure). This is an example of an experience based approach to rating.

### The office premium

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The office premium (also known as gross premium) is the theoretically correct premium that insurance companies charge policyholders.

In practice, calculations become very complicated when allowance is made for :

• reporting and settlement delays
• investment income
• changes in policy conditions and exposure
• trends in claim size and frequency

A theoretical office premium could take the risk premium as a starting point and adjust it to include loadings for commission, office expenses, unanticipated losses, reinsurance cost. The office premium should also allow for investment income earned from the investment of premium income (discounting).

The basic office premium formula is given as :

(1-k)x OP = RP*(1+d) + c*OP + FE + v*OP + VE + CF*CE + p*OP

where

• OP = Office Premium
• RP = Risk Premium
• FE = Fixed Expenses
• CF = Expected Claims Frequency
• CE = Expected Claims Expenses
• k = contingency factor for expenses arising from poor investment, over-run expenses, etc
• d = contingency factor for claims variability
• c = commission as a percentage of Office Premium
• v = variable expenses as a percentage of Office Premium
• p = explicit profit criterion as a percentage of Office Premium

The basic office premium calculation formula is to demonstrate how premium formulas are built up and is not only way that premium rating process is done. The formula may be more complicated with additional items such as investment income, reinsurance, tax, etc. The level of complexity depends on how much adjustment is made to the risk premium.

## Reserving

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Reserves are required to cover outstanding claims as well as unexpired risks.

Estimates of outstanding claims can be done on either :

• A case by case basis
• Using statistical methods at a portfolio level

There are two aspects to setting (calculating) reserves :

• Estimating future claims payments
• Applying judgement regarding the required level of prudence (conservatism)

Most statistical methods use a tabulation of claims payments by origin period (rows) and development period (columns). Assumptions regarding the stability of the past claims development pattern as well as whether or not the pattern will continue into the future are made.

Statistical method can be applied to various aspects of the claims experience that are sufficiently stable over time and measurable (e.g. claims count or claims size development).

In practise, statistical methods can be flawed by problems that can distort the results :

• Errors in the data
• Large claims
• Inflation
• Latent claims
• Catastrophes
• Changes in procedure (claims reporting, settlement)
• Changes in the mix of business written (e.g. liability vs material damage cover)
• Insufficient or inadequate data

These problems do not, however, mean that statistical methods are useless. In practise, adjustments are often made to compensate for such problems.

### The Basic chain ladder method

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The Basic chain ladder method is based on the assumption that the proportion of claims from a given origin period belonging to each development period remains constant.

The Basic chain ladder methods works as follow :

• tabulate claims cumulatively ; (e.g. C[2,3] is the sum of claims from origin period 2, that developed by development period 3)
• calculate the development ratio d[j-1,j] = sum { C[i,j] } / sum { C[i,j-1] }
• use the derived development ratios to complete the tabulation
• using the tabulation – calculate the amount of claims that will develop in future periods (for each origin year)

The Basic chain ladder method implicitly assumes that past inflation will continue into the future. The Inflation adjusted chain ladder method can be used to make explicit assumptions about future inflation levels.

There are also variants of the chain ladder method that assume a stable average cost per claim. These methods require development tables for claims count as well as tables for average claims cost.

### The Bornhuetter Ferguson method

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The Bornhuetter Ferguson method uses an assumption regarding the claims development pattern, as well as an assumption regarding the ultimate claims for each origin period. The estimate of ultimate claims is typically made using a loss ratio assumption. For each origin year : the loss ratio assumption is then divided into an historic and future component – relative to the reserving date (using the assumptions regarding claims development pattern stability).