Optimization under uncertainty with conditional Value-at-Risk

Abstract

The objective of this thesis has been the study of risk analysis and optimization under uncertainty. Theoretical aspects of several risk measures have been contemplated, and we have discussed their strengths and weaknesses. Of special interest were coherent risk measures, and in particular conditional Value-at-Risk. We have shown that this is an important risk measure which is suitable for a wide range of applications. We have studied how Value-at-Risk and conditional Value-at-Risk can be used to estimate the future risk in a financial market, and how Value-at-Risk may give unsatisfactory results in this application. When applied to the optimization of structural design, CVaR leads to beneficial compared to similar optimization under Value-at-Risk. Moreover, we have considered the optimization of reinsurance contracts, where we have shown that multivariate reinsruance contracts can be optimized using CVaR.