Dear All, I am resending you the task I got in my Risk Management class. I am stuck at solving this one. I assume you know but to make clear p(x) is some prob. distribution, VaR is value with probability alpha that any x will be <= than VaR. Expected Shortfall is expected value of x lower than VaR in assumed distribution. ES can be expressed by two forms and we should prove that thay are equivalent, can someone help me solve it? Simply VaRa where a = 0.01 gives us risk threshold (in money) that will be crosseed with 1% probability. However it can be many times higher than treshold itself, ES gives us expected value of risk crossing that treshold.
