Models and Algorithms for Risk Adjusted Optimization with Robust Utilities

本奖项的研究目标是研究由效用函数规范激发的放松单变量和多变量随机优势的概念。风险调整决策的一个主要挑战是评估与不确定结果相关的决策者的风险/效用函数。随机优势概念能够定义一个随机实体（变量、向量、矩阵、过程等）对另一个随机实体的偏好，因此可以用来比较决策选择之间的不同风险。随机优势的概念与效用理论有关，它适用于一类效用函数，其中假设决策者效用函数的先验知识有限，不幸的是，这导致了非常保守的模型。因此，迫切需要开发模型和相应的算法，以系统地规避传统效用理论的挑战，特别是当决策基于相互冲突的目标和多个随机结果时。如果成功，这项研究的结果将导致开发一类新的风险调整决策模型，这些模型将以比目前现有技术更现实的方式纳入风险。将开发计算效率高的算法来解决这些模型。

The research objective of this award is to study concepts of relaxed univariate and multivariate stochastic dominance motivated from the specification of utility functions. A major challenge in risk-adjusted decision making is the assessment of a decision maker's risk/utility function associated with uncertain outcomes. The stochastic dominance concept enables the defining of preferences of one random entity (variable, vector, matrix, process, etc.) over another and therefore can be used to compare the different risks between decision alternatives. The concept of stochastic dominance is related to utility theory, which works with a class of utility functions where limited prior knowledge on a decision maker's utility function is assumed, which unfortunately results in very conservative models. Developing models, and the corresponding algorithms, that can systematically circumvent the challenges of traditional utility theory, especially when the decision is based on conflicting objectives and multiple random outcomes, is thus critically needed.If successful, the results of this research will lead to the development of a new class of risk-adjusted decision models that incorporate risk in a more realistic way than currently existing techniques. Computationally efficient algorithms will be developed to solve these models.