We propose a novel approach for optimization and decision problems under uncertainty. We first describe it for stochastic optimization under distributional ambiguity with and without data for the random parameter. Distributional ambiguity means that an entire family $P$ of distributions is considered instead of a single one. For our approach, which avoids non-verifiable assumptions and improves upon the model accuracy, $P$ represents the integration of all kind of information at hand being more or less uncertain. This leads to a generalization of the stochastic optimization under distributional ambiguity as well as of the statistical decision approach. When searching for a really suitable solution one has to assume and accept the uncertainty as the given situation in the reality with the consequence that the optimum cannot be achieved, but at best up to an inevitable tolerance or error term. Our approach considers the problem from a completely different point of view, compared to common stochastic optimization approaches under ambiguity, namely from this error or tolerance term. In this way, with the appropriate definition of tolerance, it succeeds in minimizing this term. The result for the Statistical Decision Theory is a convincing optimality property even for finite sample sizes, an important aspect for practical applications. A solution, named c-robust, that follows the same basic principles, is developed in situations where the tolerance becomes too large for the given application but the user can identify a maximum value for this tolerance.
C-optimal AG Switzerland, March/2020