Considering the forward price \(F\) of a nondividend-paying stock, we have

\[ F_{t, T}=P_{t} e^{r(T-t)} \]

where \(r\) is the risk-free interest rate, which is constant, and \(P_{t}\) is the current stock price. Suppose \(P_{t}\) follows the geometric Brownian motion \(d P_{t}=\) \(\mu P_{t} d t+\sigma P_{t} d w_{t}\). Derive a stochastic diffusion equation for \(F_{t, T}\).