On Exponential Utility and Conditional Value-at-Risk as Risk-Averse Performance Criteria

The standard approach to risk-averse control is use the exponential utility (EU) functional, which has been studied for several decades. Like other functionals, EU encodes risk aversion through an increasing convex mapping $\varphi$ of objective costs subjective costs. An cost a realization notation="LaTeX">$y$ random variable notation="LaTeX">$Y$ . In contrast, notation="LaTeX">$\varphi(y)$ notation="LaTeX">$\varphi(Y)$ that transformed measure preferences about outcomes. For EU, transformation notation="LaTeX">$\varphi(y) = \exp(({-\theta}/{2})y)$ , and under certain conditions, quantity notation="LaTeX">$\varphi^{-1}(E(\varphi(Y)))$ can be approximated by linear combination mean variance More recently, there growing interest in using conditional value-at-risk (CVaR) functional. contrast CVaR concerns fraction its possible realizations. If continuous with finite notation="LaTeX">$E(|Y|)$ then at level notation="LaTeX">$\alpha$ expectation notation="LaTeX">$\alpha \cdot 100\%$ worst cases. Here, we study applications functionals controller synthesis safety analysis development numerical examples, emphasis on CVaR. Our contribution examine decision-theoretic, mathematical, computational tradeoffs arise when optimal analysis. We are hopeful this work will advance interpretability technology elucidate potential benefits.