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风险度量公理
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By reviewing the latest progress in the risk theory, it was considered that safety means zero risk, every matter has risk, and safety is only relative. Safety problem is indeed a problem of system risk. Risk and safety are symmetric descriptions of the same system under uncertain situation. The degree of safety or risk is not only depending on natural factors but also subjective factors. Mine pit risk set, degree of mine pit risk, and new comprehensive evaluation indexes for safety degree are derived according...

By reviewing the latest progress in the risk theory, it was considered that safety means zero risk, every matter has risk, and safety is only relative. Safety problem is indeed a problem of system risk. Risk and safety are symmetric descriptions of the same system under uncertain situation. The degree of safety or risk is not only depending on natural factors but also subjective factors. Mine pit risk set, degree of mine pit risk, and new comprehensive evaluation indexes for safety degree are derived according to the risk degree function for satisfying the axiom of risk measurement in combination with the structural analysis of the mine pit risk system. This makes the evaluation of mine safety to be established on a rational theoretical basis, in which the relative risk index could be adopted directly as the pre-warning index of mine risk.

对风险理论最新进展的评述认为 ,安全就是零风险 ,凡事总有风险 ,安全只是相对的 ;安全问题是系统风险问题 ,风险和安全是同一个系统不确定性状态的两种对称的描述 ;安全程度或风险大小不仅取决于客观自然因素也决定于主观因素。笔者根据姜青舫提出的满足风险度量公理的险度函数 ,对矿井风险体系的结构分析 ,提出了矿井风险集、矿井险度和安全度新型综合评价指标。使矿山的安全评价建立在合理风险理论的基础之上 ,其中相对险度指标可直接作为风险预警指标使用。

To solve the problen of the limits of finite probability space and static framework of coherent measure of risk,the coherent measure of risk is extended from the finite probability space into the dynamic framework on the general probability space.The concepts of acceptance set and capital requirement of risk measure in the dynamic risk measures framework are put forward according to the characters of general probability space and its measure function.Based on the concepts,the propositions on the acceptance set...

To solve the problen of the limits of finite probability space and static framework of coherent measure of risk,the coherent measure of risk is extended from the finite probability space into the dynamic framework on the general probability space.The concepts of acceptance set and capital requirement of risk measure in the dynamic risk measures framework are put forward according to the characters of general probability space and its measure function.Based on the concepts,the propositions on the acceptance set of convex risk measures on the general probability space are proposed and proved.There are also corresponding propositions on the mapping relationship between risk measure and capital requirement in the third part,which are dealt with in the same way as propositions above.Finally the poor consistency,strong consistency and recursive ness towards discrete-time process risk measures have been proposed,which constitute the axioms of dynamic risk measures on general probability space.

针对一致性风险度量有限概率空间和静态框架的限制问题,将一致性风险度量公理扩展到广义概率空间动态框架内。根据广义概率空间及其度量函数性质,在风险度量动态框架下给出风险度量可行集和资本需求的概念,并在此基础上证明广义概率空间下凸性风险度量可行集以及风险度量与资本需求映射关系的相关命题,最后提出离散过程风险度量的弱持续性、强持续性和递归性,构建广义概率空间下动态风险度量公理体系。

 
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