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How is the Arrow Debreu Price related to Green's function at an intuitive level and how is this used in practice?

Note Added 2021/02/01

I came across this in the Black Derman Toy model paper by Boyle, Seng Tian (2000) and see Green's function used without explanation in other BDT articles. Green's function is also referred to as a pricing kernel. I struggle to see how this use is related to my understanding of Green's functions in context of ODE/PDE differential operators and Dirac Delta and hence my request for an intuitive explanation.

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    $\begingroup$ This is a good question - I assume the entry of Green's functions comes from the PDE pricing methodology of derivative securities. $\endgroup$
    – rubikscube09
    Feb 1, 2021 at 19:41

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