Robustness in the Optimization of Risk Measures

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk-measurement-related optimization problem is robust, which we call “robustness against optimization.” The new notion is studied for various classes of risk measures and expected utility and loss functions. Motivated by practical issues from financial regulation, special attention is given to the two most widely used risk measures in the industry, Value-at-Risk (VaR) and Expected Shortfall (ES). We establish that for a class of general optimization problems, VaR leads to nonrobust optimizers, whereas convex risk measures generally lead to robust ones. Our results offer extra insight on the ongoing discussion about the comparative advantages of VaR and ES in banking and insurance regulation. Our notion of robustness is conceptually different from the field of robust optimization, to which some interesting links are derived.

Innovative Implementation Of Investment Insurance In The Republic Of Uzbekistan

This article examines the civil regulation of the innovative implementation of investment insurance activities in the Republic of Uzbekistan, the issues of attracting and using investments through innovative activities. The article provides definitions of the basic concepts of innovation in the field of investment insurance and legal innovation. The analysis of the civil legislation in force in the field of foreign investment insurance regulation and innovative implementation of investment insurance in the country has been carried out. Furthermore, proposals will be made to improve legislation in the field of investment insurance in the republic by introducing IT technologies in the process of investment insurance activities.