Is DeepXDE able to have a terminal condition instead of an initial

[JackDigout]

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: 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

[vl-dud]

Why don't you just add this equation to the PDEs list?

[HUKAIR]

Hi can u please show that code in solving black scholes ？