A newsvendor order decision analysis in a safety space

In a risk-averse newsvendor problem, researchers analyzed the probability distributions of profits directly to obtain the optimal decision. We begin from a viewpoint of inventory investment, discuss about the relationship between the property of capitals and risk preference. We take the maximum loss of the investment as the measurement of risk, and construct a safety space for the risk-averse decision maker. In this bound, we obtain the optimal expected utility decision under a fixed risk-taking.