Ruszczyński, Andrzej; Shapiro, Alexander Optimization of risk measures. (English) Zbl 1181.90281 Calafiore, Giuseppe (ed.) et al., Probabilistic and randomized methods for design under uncertainty. London: Springer (ISBN 1-84628-094-X/hbk). 119-157, 433-453 (2006). Summary: We consider optimization problems involving coherent measures of risk. We derive necessary and sufficient conditions of optimality for these problems, and we discuss the nature of the nonanticipativity constraints. Next, we introduce dynamic measures of risk, and formulate multistage optimization problems involving these measures. Conditions similar to dynamic programming equations are developed. The theoretical considerations are illustrated with many examples of mean-risk models applied in practice.For the entire collection see [Zbl 1085.90001]. Cited in 39 Documents MSC: 90C39 Dynamic programming 91B30 Risk theory, insurance (MSC2010) 91G40 Credit risk 91G80 Financial applications of other theories PDFBibTeX XMLCite \textit{A. Ruszczyński} and \textit{A. Shapiro}, in: Probabilistic and randomized methods for design under uncertainty. London: Springer. 119--157, 433--453 (2006; Zbl 1181.90281)