Abstract
This article addresses the issue of risk management for extreme events. The term stochastic sustainability will be defined in relation to the risk management of extreme events. On the basis of stochastic sustainability, a risk evaluation function is defined as an efficient reserve to remedy contaminations just as a premium rating in insurance policy. A term of generalized safety loading is used as a key concept to evaluate the degree of extremeness of risk. A simple model of the environmental or infrastructure systems is used to illustrate the procedure of risk evaluation where stochastic sustainability is required in case of accidental
environmental contamination. A case study of soil contamination at landfill sites is presented as an example to test this risk evaluation function.