Optimizing decisions in situations with unresolved ambiguity

点击翻译按钮获取中文摘要

Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem being addressed. This is for example the case in an inventory management problem where the future market demand for a product might be subject to change, or in a problem of portfolio selection where the future value of assets is uncertain. While there are many situations in which the nature of uncertainty can be fully characterized using distribution models, there is now a growing amount of evidence that indicates that such models are in most situation impossible to identify precisely and unequivocally. Indeed, in the era of “Big data”, it is now common practice for decision maker to extract distribution information from immense collection of historical data, yet such procedures necessarily leave one with an imprecise characterization of the distribution and of how much this distribution actually resembles the distribution of future outcomes. One might also evoke the debates and controversy that have emerged following the recent financial crisis regarding how to model the likelihood of joint realization of events (e.g. in the pricing of collateralized debt obligations) and even regarding how to quantify risk (e.g. the use of value at risk or expected shortfall in banking regulations as proposed by the Basel III accords). Both debates have serious implications for industrial engineering problems where risk needs to be mitigated.