Recently, a new approach for optimization of Conditional Value-at-Risk CVaR was suggested and tested with several applications. By de nition, CVaR, also called Mean Excess Loss, Mean Shortfall or Tail VaR, is the expected loss exceeding Value-at Risk VaR. Central to the approach is an optimization technique for calculating VaR and optimizing CVaR simultaneously. This paper extends this approach to the optimization problems with CVaR constraints. In particular, the approach is used for nance applications such as maximizing returns under CVaR constraints. A case study for the portfolio of S&P 100 stocks is performed to demonstrate how the new optimization techniques can be implemented. Historical data were used for scenario generation.

No abstract

The paper considers modelling of risk-averse preferences in stochastic programming problems using risk measures. We utilize the axiomatic foundation of coherent risk measures and deviation measures in order to develop simple representations that express risk measures via specially constructed stochastic programming problems. Using the developed representations, we introduce a new family of higher-moment coherent risk measures (HMCR), which includes, as a special case, the Conditional Value-at-Risk measure. It is demonstrated that the HMCR measures are compatible with the second order stochastic dominance and utility theory, can be efficiently implemented in stochastic optimization models, and perform well in portfolio optimization case studies.Risk measures, Stochastic programming, Stochastic dominance, Portfolio optimization,

No abstract

No abstract

No abstract

No abstract

No abstract