ABSTRACT
We approach the problem of partial hedging by minimizing conditional value-at-risk (CVaR), a quantile downside risk measure. Consider a probability space ( Ω , F , P ) $ (\iOmega ,{ \mathcal{F}},\text{ }P) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315118505/6befe1c9-a2f5-4407-a7d2-aff70ef0dad0/content/inline-math5_1.tif"/> and a choice-dependent F $ {\mathcal{F}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315118505/6befe1c9-a2f5-4407-a7d2-aff70ef0dad0/content/inline-math5_2.tif"/> -measurable random variable L(x) characterizing the loss, with strategy vector x ∊ X and strategy constraints X. We assume that E P [|L(x)|] < s for all x ∊ X, where E P means expectation w.r. to P.
