General equivalent formulas for VaR are shown here. Assuming the first one, argue that the next two are equivalent to it. [Hint: Consider a distribution $X$ that at a certain point jumps up. Then examine points to the right of the jump for a formula such as (a) or to the left for one such as (c).]

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(a) VaR -inf (m: P[X h} 11 (b) VaR = sup{y: P[X -y]> h}. (c) VaR = -sup{m: P[X