Does cummax works in a sde solver?
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I want to model a 2-dimension SDE where the drift and the diffusion are:
% solve the system
F = @(t, X) [mu*pi(y-(X(2)-z)+(X(1)-v)+max(y, cummax(X(2)-X(1)))-y, X(2))-c(y-(X(2)-z) ...
+(X(1)-v)+max(y, cummax(X(2)-X(1)))-y, X(2)); muz*X(2)];
G = @(t, X) [sigma*pi(y-(X(2)-z)+(X(1)-v)+max(y, cummax(X(2)-X(1)))-y, X(2)) 0; 0 sigmaz*X(2)];
X = sde(F, G, "StartState", x);
[X, T] = simByEuler(X, n, 'DeltaTime', dt);
Here, pi is some function that I have defined before in the code. My question is: does here cummax works on all previous values of X(2)-X(1), or it takes it as a scalar at every iteration? In particular
max(y, cummax(X(2)-X(1)))
should represent the process .
Thank you so much for your attention, I hope I made myself clear.
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回答(1 个)
Torsten
2024-6-23
编辑:Torsten
2024-6-23
My question is: does here cummax works on all previous values of X(2)-X(1), or it takes it as a scalar at every iteration?
It takes it as a scalar in each iteration because X(2)-X(1) is a scalar.
I'm not an expert in SDEs, but it seems that your equation does not belong to the class that can be solved using "sde".
2 个评论
Torsten
2024-6-24
编辑:Torsten
2024-6-24
I think even if there were a way to keep track of them, your equation cannot be solved with "sde" because F and G in the underlying equation can only depend on X_t, not on X_s for s < t.
But as said: I'm not an expert in this field - I might be mistaken. (And I also don't know how to keep track of them.)
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