A risk hypothesis and risk measures for throughput capacity in systems

A basic risk hypothesis for system throughput capacity in the presence of risk is proposed. It is expressed as a basic risk equation , derived in the paper, and governs all nongrowth, nonevolving, agent-directed systems. The basic risk equation shows how expected throughput capacity increases linearly with positive risk of loss of throughput capacity. The conventional standard deviation risk measure, from financial systems, may be used. A proposed new measure, the mean-expected loss risk measure with respect to the hazard-free case, is shown to be more appropriate for systems in general. The concept of an efficient system environment is also proposed. The well-known financial risk equation, hitherto deduced empirically, may be derived from the basic risk equation. When there is both risk exposure and resource sharing, the basic risk equation may be combined with a resource-sharing equation that governs how throughput capacity changes with the resource-sharing level. The basic risk equation also allows for risk elimination and reduction. All quantities in the equation are precisely defined, and their units are specified. The risk equation reduces to a useful numerical expression in practice.