I work with stock price time series where I check for structural breaks in the series. To do that I fit simple models such as AR and ARIMA.
However, I was proposed to express the stock price in terms of not classic time series models but in terms of (system of), possibly stochastic, differential equations. The idea is that the model should be similar to Black&Scholes. However, the BS model is about option price, not stock price, so I cannot use it (plus, if I am not mistaken, the stock price is a Brownian motion that is a random variable, so cannot be predicted). I failed to find publications that show the details.
Can anyone suggest a way or literature regarding how time series can be expressed or forecasted using DE?