Does cummax works in a sde solver?

2 views (last 30 days)
Salvatore Bianco on 23 Jun 2024
Edited: Torsten on 24 Jun 2024
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.

Torsten on 23 Jun 2024
Edited: Torsten on 23 Jun 2024
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 CommentsShow NoneHide None
Salvatore Bianco on 24 Jun 2024
So, there is a method I can use that keeps track of all previous values?
Torsten on 24 Jun 2024
Edited: Torsten on 24 Jun 2024
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.)

Categories

Find more on Stochastic Differential Equation (SDE) Models in Help Center and File Exchange

R2024a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!