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Introduction

1.1 What is Reinsurance?

A reinsurance contract is an agreement in which one party (the reinsurer) agrees to indemnify another party (the reinsured, the first-line insurer or also the ceding company, cedent) for specified parts of its underwritten insurance risk. In turn, the cedent pays to the reinsurer a reinsurance premium for this service. That is, in reinsurance the principle of insurance is lifted up one level, so an insurance company seeks itself the possibility of replacing parts of its future loss by a fixed premium payment (much like a policyholder does when entering an insurance contract). There are many reasons why such a risk transfer from the insurer to the reinsurer can be desirable for both parties, as well as for the economy in general, and we will outline a number of them in Section 1.2.

While reinsurance can be seen as a particular form of insurance, and naturally shares various common features with it, reinsurance is also quite distinct from primary insurance in a number of aspects. These include the type and magnitude of risks under consideration, the type of data available for the risk analysis, the diversification possibilities, demand/supply peculiarities of contracts quite different from the primary insurance market, and also the fact that reinsurance is a form of risk sharing among two "professional" insurance entities, so that the necessary guidelines for regulation can be quite different.

(Non-life) reinsurance contracts are typically written for one year, and one distinguishes between obligatory treaties, where a binding agreement is specified that applies to all risks of a specified risk class, and facultative arrangements, which are negotiated on each individual risk. A facultative treaty is then a contract where the cedent has the option to cede and the reinsurer has the option to decline or accept classified risks of a particular business line. In practice many contracts actually involve several reinsurers (e.g., the contract is negotiated with a primary reinsurer, and other reinsurers then participate proportionally in the reinsurance coverage, or a second reinsurance contract with another reinsurer is written for parts of the remaining risk of the cedent after a first contract). The relationship between insurer and reinsurer is often of a long-term nature, which also has an effect on the way reinsurance premiums are negotiated. Finally, there is no relation between a reinsurer and the individual policyholders of the underlying risks. A reinsurer may itself enter a reinsurance contract with another insurance company on parts of the reinsured risk, and such a procedure is called retrocession.

Table 1.1 gives a feeling for the size of the global reinsurance market in comparison to the primary insurance market. One sees that in terms of premium volume, reinsurance is only employed for a small fraction of the primary insurance risk. However, typically the reinsured risk is the one that is complicated to assess and handle (this is one of the main reasons why it is reinsured!), which makes this type of risk particularly challenging for actuaries, statisticians, and other risk professionals. Worldwide, there are about 200 reinsurance companies today, and many of these are also acting as primary insurers in the market.

Table 1.1 Global premium volume 2015 (in US$ billions).

Source: SwissRe.

1.2 Why Reinsurance?

Let us look at why an insurance company is interested in buying reinsurance. The main function of insurance companies is to take risk. This is similar to the business model of other financial organizations, and both types leverage the capital provided by shareholders through raising debt. However, insurers raise debt by selling policies to insureds, which makes the debt very risky (due to uncertainty around the timing and severity of claims), whereas financial debt would typically rather have pre-determined expiry and face value (severity). This leveraging activity is a competitive advantage, but also makes the companies vulnerable to distress and insolvency, creating the demand for risk management. Among the available risk management tools, risk transfer through reinsurance then plays an important role in improving the company's overall risk profile. Let us look at some of the main motivations for the insurer to buy reinsurance as a means of risk transfer (several of which are not independent of each other):

• Reducing the probability to suffer losses that are hard to digest
  This is a rather general statement and many of the items below are in fact refinements of this criterion. It should be kept in mind that for an insurance company buying reinsurance means passing on some of its insurance business (i.e., its core activity), and hence typically the goal is to keep the reinsured part small. However, reduction of risk exposure can be desirable or necessary for the reasons outlined below.
• Stabilizing business results
  Entering a reinsurance contract reduces the volatility of the cedent's financial result, as random losses are replaced by a (typically deterministic) premium payment. That is, reinsurance can be a means to steer the volatility of an insurance company towards a desired level, and the latter can have particular advantages (e.g., with respect to taxes, capital requirements and market expectations).
• Reducing required capital
  Reducing the aggregate risk will reduce the required capital to bear such risks, and in view of capital costs this may be desirable. Concretely, if the reinsurance premium (together with the administration costs) is smaller than the gain resulting from the corresponding reduction of capital, the reinsurance contract is desirable. In fact, due to the ongoing shift towards risk-based regulation, the notion of capital and its management becomes a central issue for insurance companies, and reinsurance then should be understood as a tool in this context. This corresponds to an important finance function of reinsurance as a substitute for capital, freeing up capacity.
• Increasing underwriting capacity
  In the presence of a reinsurance contract, only a certain part of the risk is assumed by the insurer, and hence under otherwise identical conditions an insurance company can afford to underwrite more and larger policies (see Chapter 2 for details), which may be desirable for various reasons, including market share targets, testing and entering of new markets, gaining (data) experience in certain business lines or regions etc. It also can lead to enhanced liquidity.
• Accessing benefits from larger diversification pools
  Often the primary insurers' business model is restricted to a local area, in which case attempts to look on their own for diversification possibilities outside of that market for the more dangerous part of the risks would be very costly and inefficient. Reinsurers, on the other hand, typically act on an international level and therefore have more possibilities for diversifying such risks. Consequently the amount of capital needed to safeguard these risks in the portfolio can be considerably lower for a reinsurer and so the risk transfer produces economic gain through attractive reinsurance premiums.

We mention a few further motivations:

• Reducing tax payments
  Equalization reserves (i.e., reserves for volatility of claims and their arrivals over longer time periods, which is, for instance, particularly important for catastrophe risks) of insurance companies are taxed in most legislations. If such reserves are paid to a reinsurance company in the form of a reinsurance premium (or, alternatively, into a respectively created captive structure, cf. Section 10.2), then the taxation pattern becomes more favorable, as for reinsurers and captives (often located in tax-favorable countries) different tax rules may apply.
• Other legal issues
  Reinsurance can be a helpful tool to resolve legal constraints such as regulatory compliance. For instance, if an insurance company does not have a formal license to write business in a certain country, a solution can be to find a local insurer with such a license and act as a reinsurer for this local company.
• Financial solutions
  The reinsurer can serve as a facilitator for financial solutions. Examples include reducing (expected) financial distress costs by providing run-off solutions (cf. Section 10.2) and portfolio transfers to other companies or the capital markets as well as setting up securitization transactions like issuing bonds.
• Protection against model risk
  Insurance activities are designed on the basis of stochastic models for the underlying risks. For the aggregate performance, both the understanding of the marginal risks as well as of the dependence between them is important.1 However, every model is an imperfect description of reality, and the less experience and data one has, the higher the uncertainty about whether the model underlying the business plan is appropriate. Reinsurance is a way to mitigate model inadequacy (e.g., concerning the tails of the risks or their dependence).
• Support in risk...