# Can I use Mathematica to derive these induction equations? [closed]

I have the following model

$D_T=D_0+\varepsilon\&space;_1+\ldots+\varepsilon\&space;_T,&space;where&space;\varepsilon_t\sim&space;N\left(0,\sigma_\varepsilon^2\right),&space;i.i.d&space;over&space;time.$

T + 1 dates, t = 0, 1, ...,T

$\mathbb{E}_t^e\left(P_{t+1}-P_t\right)=X_t\equiv\left(1-\theta\right)\sum_{k=1}^{t-1}{\theta^{k-1}\left(P_{t-k}-P_{t-k-1}\right)}+\theta^{t-1}X1$

$N_t^e=\frac{X_t}{{\gamma\sigma}_\epsilon^2}$

$N_t^f=\frac{\mathbb{E}_t^f\left(P_{t+1}-P_t\right)}{{\gamma\sigma}_\epsilon^2}$

$N_{t-1}^f=\frac{D_{t-1}-P_{t-1}}{{\gamma\sigma}_\epsilon^2}$

$N_{t-1}^f*\mu^f&space;+&space;N_{t-1}^e*\mu^e&space;=Q$

$P_{t-1}=D_{T-1}&space;+&space;\frac{\mu^e}{\mu^f}*\sigma_{\epsilon}^2*\gamma*N_{T-1}^e-\frac{\sigma_{\epsilon}^2*\gamma*Q}{\mu^f}&space;\\\\\rightarrow&space;N_{T-2}^f=&space;\frac{D_{T-2}-\sigma_{\epsilon}^2*\gamma*Q-P_{T-2}}{\sigma_{\epsilon}^2*\gamma}&space;\\&space;\mu^e*N_{-2}^e+\mu^f*N_{-2}^f&space;\\&space;\rightarrow&space;P_{t-2}=D_{T-2}&space;+&space;\frac{\mu^e}{\mu^f}*\sigma_{\epsilon}^2*\gamma*N_{T-2}^e-\frac{\sigma_{\epsilon}^2*\gamma*Q}{\mu^f}&space;\\Continuing&space;\&space;backward&space;\&space;induction&space;\&space;leads\&space;to&space;\\\\&space;N_t^f&space;=&space;\frac{D_t-(T-t-1)\sigma_{\epsilon}^2*\gamma*Q-P_t}{\sigma_{\epsilon}^2}&space;\\\\&space;P_t=D_t+\frac{\mu^e}{\mu^f}X_t-\gamma\sigma_\varepsilon^2Q\left(T-t-1+\frac{1}{\mu^f}\right)$

This was all solved by hand and I wanted to ask if Mathematica can be used to do the job instead?

If so, what commands are helpful?

## closed as unclear what you're asking by Mariusz Iwaniuk, rhermans, m_goldberg, Edmund, RomanJul 12 at 9:12

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Maybe, you'd have to provide a clear description of symbols used and convention etc. There is also a standard question: have you tried anything? – Kuba Jul 12 at 8:41
• @Kuba This more of a general question. I am not looking for any code solution. I am just wondering if Mathematica is able to something like backward induction. I looked online for it but couldn’t find anything – Jj Blevins Jul 12 at 8:44