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I'm currently trying to use DeepXDE to solve the Black-Scholes equation for one space dimension and then higher ones after that. It is as follows: Black-Scholes Equation $$\frac{\partial V}{ \partial t } + \frac{1}{2}\sigma^{2} S^{2} \frac{\partial^{2} V}{\partial V^2} + r S \frac{\partial V}{\partial S}\ - r V = 0$$
and for the N-dim case it is $$\frac{\partial V}{\partial t} + \frac{1}{2} \sum_{i, j = 1}^{N} \sigma_i\sigma_j S_i S_j \rho_{i,j} \frac{\partial^2V}{\partial S_i \partial S_j} + \sum_{i = 1}^{N} r_i S_i \frac{\partial V}{\partial S_i} - rV = 0$$
My issue is that it has a terminal condition: $$V(S,T) = max(S_T - K, 0)$$ instead of an initial condition. Is it possible to have this work in DeepXDE and if so how?
Thanks
The text was updated successfully, but these errors were encountered:
Hi,
I'm currently trying to use DeepXDE to solve the Black-Scholes equation for one space dimension and then higher ones after that. It is as follows:
$$\frac{\partial V}{ \partial t } + \frac{1}{2}\sigma^{2} S^{2} \frac{\partial^{2} V}{\partial V^2} + r S \frac{\partial V}{\partial S}\ - r V = 0$$
Black-Scholes Equation
and for the N-dim case it is
$$\frac{\partial V}{\partial t} + \frac{1}{2} \sum_{i, j = 1}^{N} \sigma_i\sigma_j S_i S_j \rho_{i,j} \frac{\partial^2V}{\partial S_i \partial S_j} + \sum_{i = 1}^{N} r_i S_i \frac{\partial V}{\partial S_i} - rV = 0$$
My issue is that it has a terminal condition:$$V(S,T) = max(S_T - K, 0)$$ instead of an initial condition. Is it possible to have this work in DeepXDE and if so how?
Thanks
The text was updated successfully, but these errors were encountered: