Stephen Mildenhall


Property Casualty Coverages

Commercial Coverages

Personal Lines Coverages


A reinsurance company insures risks assumed by a primary insurance company. The reinsurer assumes the risk, the reinsured company, or cedent, cedes the risk. The primary company retains the part of the risk it does not cede.

The reinsurer has a contract with the cedent but not the cedent's clients.

Reinsurance on reinsurance is called a retrocession.

Why do primary companies purchase reinsurance?

Treaty vs. Facultative Reinsurance

Treaty reinsurance covers a set of subject policies for a given period of time. Subject policies are often defined in terms of lines of business, e.g. "all commerical auto liability policies" or "all homeowners policies".

Facultative reinsurance covers a single underlying insured. Unlike a treaty, facultative ("fac") reinsurance is underwritten by the reinsurer one account at a time.

Quota Share vs Excess of Loss

Under a Quota Share reinsurance contract, a fixed percentage of the premiums and a fixed percentage of the losses are ceded to the reinsurer. For this reason, quota shares are called proportional reinsurance. The reinsurer typically allows a ceding commission to the cedent to cover costs of producing the business. The level of the ceding commission ("cede") is essentially the only pricing variable in a simple quota share deal.

Under an Excess of Loss reinsurance contract the reinsurer covers losses in excess of an attachment, so the recovery is not directly proportional to the cedent's loss. Thus Excess of Loss contracts are non-proportional. Excess of Loss ("XOL") contracts can cover losses in many different ways.


A typical reinsurance program for a small insurance company, or independently run department of a larger company, may look something like:

Business Written:

Reinsurance Program:

  1. Fac on all property policies to bring retention down to $1M. E.g. on a $25M property the company would buy a per risk XOL cover of $24M excess a $1M retention.
  2. Fac on all AL and GL policies to bring retention down to $250,000. E.g. on a $1M policy the company would buy a $750,000 excess $250,000 per occurrence XOL cover.
  3. Fac $9.75M excess $250,000 on all WC policies. (WC is written without policy limits, though claims in excess of $5M are very rare.)
  4. A per occurence property catastrophe treaty covering $45M excess $5M.
  5. A 50% quota share on the retained liability lines with a 30% ceding commission.

Pricing: the Actuary's Role

Insurance Pricing

Rating Method Regulation Flexibility Applies to
Manual Rating Highly regulated by State Low Personal Lines

+ schedule credits/debits

    Small Commerical
+ experience credits/debits     Medium Commerical
Loss Rating Essentially unregulated High Large commerical, unusual risks, reinsurance

Manual rating creates rates for statistical classes and uses very objective criteria to determine rates. Actuarial involvement is in setting the rates (for all insureds). No involvement in individual account pricing.

Experience and schedule credits/debits give the underwriters more flexibility in determining a rate. Actuarial involvements tends to be in setting underlying manual rates and designing procedures for experience rating.

Loss Rating: scope for actuarial involvement in individual account pricing (each treaty or certificate for reinsurance).

Reinsurance Pricing: Treaty Quota Share

What is the loss ratio? What are reinsurer's expenses? What is the ceding commission?

Reinsurance Pricing: Fac XOL

See Exhibit 1.

Reinsurance Pricing: Treaty XOL

Two key differences with Fac XOL:

  1. Do all the underlying risks expose the treaty? For example, primary company writes $500,000, $1M and $2M policy limits. A treaty $1M excess of $1M would only be exposed by the $2M policy limits---which may account for a relatively small proportion of the premium. Problem is more pronounced for property.
  2. Rate is determined as a percentage of the underlying premium. On most of the risks covered, the reinsurer doesn't actually know what the ceding company will charge! Introduces a big pricing risk for reinsurers (see last night's talk).

Treaties often contain complicated policy terms which make pricing difficult. The following give an example of some of the more common features:

To price all of these special features requires knowing the probability distribution of aggregate losses or aggregate loss distribution. Determining aggregate distributions is a central question in actuarial science and is usually addressed in a couse on Risk Theory. For an excellent survey of computing aggregate loss distributions see Wang.

Connection to Options

The payments on an excess of loss reinsurance contract or a primary insurance policy with a deductible are similar to the payoff from a call option (the right to buy). For these reasons option pricing techniques are sometimes mentioned as applicable to reinsurance pricing. However, there are some very important differences between insurance and reinsurance on the one hand and options pricing on the other. See my paper Mildenhall for a more in-depth discussion.