Risk budgeting is in connection with positive portfolio managers, so the risk we budget and control is mainly stemmed from relative risk, but not from absolute risk.

The paper considers the MLEs of expected frequencies for relative risk under simple order restrictions,and gives an iterative algorithm to compute the restricted MLEs,and proves the convergence of the algorithm.

For commonly used benchmark portfolio,risky assets are still priced by CAPM in spite of the fact that investors utility functions are expanded to include relative risk.

Through combining the pipeline statistical date with the expert opinion and taking Jingbian-Yinchuan natural gas transport plumbing as an example,the pipeline safe analog computation was carried out and a quantitative analysis of the relative risk scores of the pipeline made to seek a way to enhance the pipeline safety.

This paper obtained the Bayesian Nash equilibium bidding strategy for first price sealed bid auctions and procurments in civil engineering for some frequently used utility functions such as constant relative risk and constant absolute risk and logarithmic utility.

The calculation of value at risk when cumulative investment and interest rate is correlative stochastic processes is discussed, and the concept and its calculation of relative value at risk is proposed.