1.1. In the different versions of the “Theory of Risk” it is almost universally assumed that ruin or bankruptcy marks the end of the game. The earlier versions of the theory tried to estimate the probability of this event, and studied the steps which an insurance company could take to bring probability of ruin down to an acceptable level. The more modern versions of the theory of risk tend to formulate the problem in economic terms, and study the cost of postponing or avoiding ruin.In a recent discussion of a paper [4] surveying the development of the theory of risk, Professor Bather suggested that ruin may not necessarily be the end. If an otherwise sound insurance company gets into difficulties, so that ruin looms large, it is very likely that steps will be taken to rescue the company, for instance by refinancing, or in more extreme cases, by a merger.1.2. To practical insurance men the simple suggestion of Professor Bather may seem next to trivial. Insurance companies get into difficulties fairly regularly, and rescue operations are considered in the insurance world, if not daily, at least annualy. The suggestion has, however, far-reaching implications for the theory of risk, and these do not seem to have been fully realised. If ruin does not mean the end of the game, but only the necessity of raising additional money, the current theories of risk may have to be radically revised. In this paper we shall discuss some of these implications.
The probability of ruin in a reinsurance risk model with m-dependence assumptions
