In this paper, we examine the framework to estimate financial risk called conditional-value-at-risk (CVaR) and examine models to optimize portfolios by minimizing CVaR. We note that total risk can be a function of multiple risk factors combined in a linear or nonlinear forms. We demonstrate that, when using CVaR, several common nonlinear models can be expressed as second order cone programming problems and therefore efficiently solved using modern algorithms. This property is not shared with the more classical estimation of financial risk based on value-at-risk.
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