ABSTRACT
The process of redistribution of risk, starting with purchasing insurances by individual clients, continues at the next level: insurance companies redistribute the risk they incurred between themselves. Such a risk redistribution may be even more flexible than that at the first level: the companies may share individual risks in different ways or redistribute total accumulated risk. A common practice is to protect the portfolio against excessive claims although there are many other forms of reinsurance. A company which reinsures a part of its risk plays the role of a cedent, while the company
which assumes this part is a reinsurer. Section 1 concerns optimal forms of reinsurance and the amount to be retained from the standpoint of the cedent. In Section 2, we consider the negotiation process between two companies sharing a risk.
In this case, each company is a cedent and reinsurer simultaneously, and the result of the negotiation is based on principles equally acceptable to both companies. At least theoretically, these principles are not necessarily connected with payments for
reinsurance. The negotiation may be direct, and the companies may agree with a certain form of risk distribution without paying each other for reinsurance. However, when many companies are simultaneously involved in reinsurance, market price mechanisms are the most, if not the only, realistic mechanisms of exchanging risk. Actual reinsurance practice contains various combinations of forms of reinsurance: mu-
tual agreements on direct reinsurance, trading risks, some financial products as special options, futures, or bonds. (See, e.g., [28], [37, Section 8.7], and references therein.) However, in any case, this is a market where commodities to be exchanged are risks. We touch on this question in Section 3. The exposition below may be called fragmentary. Our goal is not to build a comprehen-
sive theory but rather to make the reader acquainted with some basic notions and to give some examples.
