Risk management on large spaces can be quite different than what we expect. For instance, risk diversification cannot easily be verified and validated on large spaces. One approach to risk management, regardless of the size of the space, is to use risk measures. While the risk measures on large spaces are fairly (well-)discussed in the literature, to my best knowledge there is none on preference relation on large spaces. In this talk, first I will discuss the implications of studying preference relations on large spaces. Then, I introduce and study monotone monetary preference relations on large spaces. I will show that any monotone risk-order can be induced by a unique minimal certain-equivalent risk measure. In other words, as far as an agent knows how to monotonically rank the risk, for a given risk variable the minimum capital requirement is uniquely determined. Furthermore, it is shown that certain-strict monotonicity is a necessary and sufficient condition under which the minimal and the maximal certain-equivalent risk measures are equal. We will also discuss natural risk measures that are introduced on large spaces.