Given two random variables X and Y and let K be a constant value. Assume the expectation E[X(Y−K)+] is given for all possible values of K≥0. Is there a way to derive the joint probability distribution of X and Y from this??
The expectation can be written as
E[X(Y−K)+]=∫∞−∞∫∞−∞x(y−K)+dF(x,y) and when density exists =∫∞−∞∫∞Kx(y−K)f(x,y)dxdy
Both marginal distributions FX and FY are known and densities exists as well. Is there any way I can derive the joint distribution if the expected value is given for all values of K?
I have been stuck on this for a while now, even rough approximations would be of much use to me or a collection of properties that can be solved numerically.
Can someone please help me?
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